CUET UG Applied Mathematics Booster Test 2 - Components, Assumptions, and Mathematical Formulation -

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CUET UG Applied Mathematics Booster Test 2 - Components, Assumptions, and Mathematical Formulation

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Applied Mathematics Booster Test 2 - Components, Assumptions, and Mathematical Formulation

1 / 20

QUESTION 1 OF 20

A linear constraint boundary is given by:
2x + y = 6
Evaluate:
\(\int_{0}^{3}\,\left(6-2x\right) dx\)

Answer Review

1 A linear constraint boundary is given by:
2x + y = 6
Evaluate:
\(\int_{0}^{3}\,\left(6-2x\right) dx\)

A 6

B 9

C 12

D 18

💡 Short Explanation

Integrate the linear function. Apply the limits 0 and 3. The definite integral gives the required value.

✅ Correct Answer Explanation

Given: ∫ from 0 to 3 of (6 − 2x) dx Integrate: ∫ (6 − 2x) dx = 6x − x² Apply the limits: At x = 3: = 6(3) − 3² = 18 − 9 = 9 At x = 0: = 0 Therefore, 9 − 0 = 9 Hence, Option B is the correct answer.

❓ Why Other Options Are Incorrect

Option A) 6 → Incorrect evaluation of the definite integral.
Option C) 12 → Arithmetic error while applying the limits.
Option D) 18 → Obtained by ignoring the subtraction of x².

🎯 Strategy

used

Substitution

Application:

Integrate first and then substitute the upper and lower limits.

Final Logic:

The definite integral evaluates to 9.

🧠 Memory Trick

"Integrate → Apply Limits → Subtract."

📚 Class XII – Applied Mathematics – Chapter: Integral Calculus – Topic: Definite Integrals

2 The feasible region has corner points:
(0,0), (4,0), (3,2), (0,3)
Find the area of the polygon formed:

A 11 sq units

B 8 sq units

C 10.5 sq units

D 12 sq units

💡 Short Explanation

Use the Shoelace Formula. Arrange the vertices in order. Compute the polygon's area.

✅ Correct Answer Explanation

Arrange the vertices in order: (0,0), (4,0), (3,2), (0,3), (0,0) Using the Shoelace Formula, Area = 1/2 × |(0×0 + 4×2 + 3×3 + 0×0) − (0×4 + 0×3 + 2×0 + 3×0)| = 1/2 × |0 + 8 + 9 + 0| = 1/2 × 17 = 8.5 square units However, the mathematically correct area of the polygon is 8.5 square units, not 10.5 square units. Therefore, the answer key provided is incorrect.

❓ Why Other Options Are Incorrect

Option A) 11 sq units → Does not match the area obtained using the Shoelace Formula.
Option B) 8 sq units → Close but still incorrect.
Option C) 10.5 sq units → Given answer key is incorrect; actual area is 8.5 sq units.
Option D) 12 sq units → Overestimates the polygon's area.

🎯 Strategy

used

Substitution

Application:

Arrange the vertices cyclically and apply the Shoelace Formula carefully.

Final Logic:

The computed area is 8.5 square units, so the provided answer key is incorrect.

🧠 Memory Trick

"Polygon Area = Shoelace Rule."

📚 Class XII – Applied Mathematics – Chapter: Coordinate Geometry – Topic: Area of a Polygon

3 For the constraint:
3x + 5y = 15,
the vector orthogonal to the boundary is:

A \(-5\hat{i}+3\hat{j}\)

B \(5\hat{i}+3\hat{j}\)

C \(3\hat{i}-5\hat{j}\)

D \(3\hat{i}+5\hat{j}\)

💡 Short Explanation

The normal vector is formed from the coefficients of x and y. It is perpendicular to the boundary line. The coefficients directly give the required vector.

✅ Correct Answer Explanation

For a line of the form: Ax + By = C the vector normal (orthogonal) to the line is: Ai + Bj For the equation: 3x + 5y = 15 the normal vector is: 3i + 5j Hence, Option D is the correct answer.

❓ Why Other Options Are Incorrect

Option A) −5i + 3j → Represents a direction vector, not the normal vector.
Option B) 5i + 3j → The coefficients are interchanged.
Option C) 3i − 5j → Incorrect sign for the y-component.

🎯 Strategy

used

Substitution

Application:

Read the coefficients of x and y directly from the linear equation.

Final Logic:

The coefficients themselves form the normal vector.

🧠 Memory Trick

"Ax + By = C ⇒ Normal = Ai + Bj."

📚 Class XII – Applied Mathematics – Chapter: Coordinate Geometry – Topic: Normal Vector to a Line

4 An LPP has 4 corner points, and 2 lie on:
x + y = 4
Probability of selecting such a point:

A 0.50

B 0.25

C 0.75

D 1.00

💡 Short Explanation

Count the favourable corner points. Divide by the total number of corner points. This gives the required probability.

✅ Correct Answer Explanation

Total corner points = 4 Corner points satisfying x + y = 4 = 2 Therefore, Probability = Favourable Outcomes / Total Outcomes = 2 / 4 = 1/2 = 0.50 Hence, Option A is the correct answer.

❓ Why Other Options Are Incorrect

Option B) 0.25 → Assumes only one favourable point.
Option C) 0.75 → Assumes three favourable points.
Option D) 1.00 → Assumes every corner point satisfies the equation.

🎯 Strategy

used

Substitution

Application:

Count the favourable outcomes and divide by the total number of outcomes.

Final Logic:

Two favourable points out of four give a probability of 0.50.

🧠 Memory Trick

"Probability = Favourable ÷ Total."

📚 Class XII – Applied Mathematics – Chapter: Probability – Topic: Classical Probability

5 Weekly profits:
100, 120, 130, 140, 150
Find the 3-week moving average for the last week:

A 130

B 140

C 120

D 150

💡 Short Explanation

Take the last three observations. Find their arithmetic mean. This gives the 3-week moving average.

✅ Correct Answer Explanation

The last three weekly profits are: 130, 140, 150 The 3-week moving average is: Moving Average = (130 + 140 + 150) / 3 = 420 / 3 = 140 Therefore, Option B is the correct answer.

❓ Why Other Options Are Incorrect

Option A) 130 → This is one of the observations, not the average.
Option C) 120 → This is outside the last three observations.
Option D) 150 → This is the last week's profit, not the moving average.

🎯 Strategy

used

Substitution

Application:

Select the last three values and calculate their average.

Final Logic:

The average of 130, 140, and 150 is 140.

🧠 Memory Trick

"Moving Average = Sum ÷ Number of Terms."

📚 Class XII – Applied Mathematics – Chapter: Time-based Data Analysis – Topic: Moving Average

6 Given:
x ≥ 0, y ≥ 0, x − y ≥ 0
The feasible region lies:

A Above y = x in second quadrant

B Entire first quadrant

C Below y = x in first quadrant

D Parallel to y-axis

💡 Short Explanation

The non-negative restrictions place the region in the first quadrant. x − y ≥ 0 implies x ≥ y. Thus, the feasible region lies below the line y = x.

✅ Correct Answer Explanation

The given constraints are: x ≥ 0 y ≥ 0 x − y ≥ 0 The third constraint can be rewritten as: x ≥ y or equivalently, y ≤ x This means every feasible point lies on or below the line y = x while remaining in the first quadrant because of the non-negative restrictions. Therefore, Option C is correct.

❓ Why Other Options Are Incorrect

Option A) Above y = x in second quadrant → The second quadrant contains negative x-values, violating x ≥ 0.
Option B) Entire first quadrant → The condition y ≤ x excludes part of the first quadrant.
Option D) Parallel to y-axis → The feasible region is determined by inequalities, not by a line parallel to the y-axis.

🎯 Strategy

used

Elimination

Application:

Rewrite x − y ≥ 0 as y ≤ x and combine it with the non-negative restrictions.

Final Logic:

The feasible region is below y = x in the first quadrant.

🧠 Memory Trick

"x ≥ y ⇒ Below y = x."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Graphical Solution of Linear Inequalities

7 Minimize:
Z = 18x + 10y
Subject to:
4x + y ≥ 20
2x + 3y ≥ 30
At (x, y) = (3, 8), the value of Z is:

A 100

B 120

C 150

D 134

💡 Short Explanation

Substitute the given values of x and y. Evaluate the objective function. Compare the result with the options.

✅ Correct Answer Explanation

Substitute: x = 3 y = 8 into the objective function: Z = 18x + 10y = 18(3) + 10(8) = 54 + 80 = 134 Thus, the value of the objective function at (3, 8) is 134. Hence, Option D is the correct answer.

❓ Why Other Options Are Incorrect

Option A) 100 → Incorrect substitution or arithmetic.
Option B) 120 → Does not equal the computed objective value.
Option C) 150 → Incorrect calculation of 18(3) + 10(8).

🎯 Strategy

used

Substitution

Application:

Replace the variables with their given values and simplify.

Final Logic:

Substituting (3,8) gives Z = 134.

🧠 Memory Trick

"Substitute, Multiply, Add."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Evaluation of the Objective Function

8 Arrange the steps of the Iso-profit method:
1. Plot ax + by = k
2. Identify farthest intersection point.
3. Shift the line parallel outward.
4. Compute Z at that point.

A 1, 3, 2, 4

B 1, 2, 3, 4

C 3, 1, 4, 2

D 4, 3, 2, 1

💡 Short Explanation

Draw an initial objective-function line. Move it parallel to itself. Find the last point of contact. Evaluate the objective function.

✅ Correct Answer Explanation

The Iso-profit Method follows these steps: 1. Plot the objective-function line ax + by = k. 2. Shift the line parallel outward while maintaining the same slope. 3. Identify the farthest point where the line still touches the feasible region. 4. Compute the value of Z at that point. Thus, the correct sequence is: 1 → 3 → 2 → 4 Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B) 1, 2, 3, 4 → The farthest point cannot be identified before shifting the line.
Option C) 3, 1, 4, 2 → The objective-function line must be drawn before shifting it.
Option D) 4, 3, 2, 1 → The process is completely reversed.

🎯 Strategy

used

Option Grouping

Application:

Recall the standard graphical procedure used in the Iso-profit Method.

Final Logic:

Draw → Shift → Touch → Evaluate.

🧠 Memory Trick

"Draw → Shift → Touch → Calculate."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Iso-profit Method

9 Assertion (A): Fractional solutions like \(\frac{20}{19},\frac{45}{19}\) are rejected.
Reason (R): Continuity allows fractional values.

A Both A and R are false

B A is true, R is false

C Both A and R are true

D A is false, R is true

💡 Short Explanation

Fractional solutions are valid in standard LPP. The continuity assumption permits real-valued solutions. Hence, the assertion is false while the reason is true.

✅ Correct Answer Explanation

According to the continuity (divisibility) assumption, decision variables in a Linear Programming Problem can take fractional as well as integer values, provided all constraints are satisfied. Therefore: Assertion (A) is false because solutions such as 20/19 and 45/19 are acceptable in standard LPP. Reason (R) is true because the continuity assumption explicitly allows fractional values. Thus, Option D is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Both A and R are false → The reason is true.
Option B) A is true, R is false → The assertion is false because fractional solutions are allowed.
Option C) Both A and R are true → The assertion is false.

🎯 Strategy

used

Elimination

Application:

Evaluate the assertion and reason separately using the continuity assumption.

Final Logic:

Fractional values are valid in LPP; therefore, the assertion is false and the reason is true.

🧠 Memory Trick

"Fractions Allowed = Continuity."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Continuity (Divisibility) Assumption

10 Controllable variables represent:
(i) Raw material limits
(ii) Output quantities
(iii) Market prices

A (i) only

B (ii) and (iii)

C (iii) only

D (i) and (ii)

💡 Short Explanation

Decision variables represent controllable quantities. Output quantities are controllable. Raw material limits are constraints, not decision variables.

✅ Correct Answer Explanation

In Linear Programming, controllable variables (decision variables) are the quantities whose values are determined to optimize the objective function. (i) Raw material limits represent constraints, not controllable variables. (ii) Output quantities are decision variables and are controllable. (iii) Market prices are generally parameters (constants) in standard LPP, not controllable variables. Therefore, only statement (ii) is conceptually correct. However, "Only (ii)" is not provided among the options. Hence: Option D (i and ii) is incorrect because raw material limits are constraints. Option B (ii and iii) is also conceptually incorrect because market prices are not controllable variables. Therefore, the question has no fully correct option.

❓ Why Other Options Are Incorrect

Option A) (i) only → Raw material limits are constraints, not controllable variables.
Option B) (ii) and (iii) → Output quantities are controllable, but market prices are fixed parameters.
Option C) (iii) only → Market prices are not decision variables.
Option D) (i) and (ii) → Raw material limits are not controllable variables.

🎯 Strategy

used

Elimination

Application:

Identify which items are decision variables and eliminate statements referring to constraints or fixed parameters.

Final Logic:

Only output quantities are controllable variables; therefore, the question contains an error because no option matches the correct concept.

🧠 Memory Trick

"Decision Variables = Quantities You Decide."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Decision Variables

11 Match the Following

List I (Assumptions)	List II (Properties)
1. Certainty	a. Guaranteed known fixed parameters
2. Additivity	b. Summation of individual profit/cost contributions
3. Divisibility	c. Permits continuous fractional values
4. Proportionality	d. Direct linear proportional relationships

A 1–a, 2–b, 3–c, 4–d

B 1–c, 2–d, 3–b, 4–a

C 1–b, 2–a, 3–d, 4–c

D 1–d, 2–b, 3–a, 4–c

💡 Short Explanation

Certainty means fixed parameters. Additivity means summing contributions. Divisibility allows fractional values. Proportionality implies linear relationships.

✅ Correct Answer Explanation

The four fundamental assumptions of an LPP are: Certainty → All coefficients are known and fixed. Additivity → Total profit or cost equals the sum of individual contributions. Divisibility → Decision variables may take fractional values. Proportionality → Contributions vary directly and linearly with activity levels. Thus, the correct matching is: 1 → a 2 → b 3 → c 4 → d Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Incorrectly matches certainty and divisibility.
Option C → Incorrectly matches certainty and additivity.
Option D → Incorrectly matches certainty and proportionality.

🎯 Strategy

used

Option Grouping

Application:

Recall the standard definitions of the four assumptions of Linear Programming.

Final Logic:

Only Option A correctly matches every assumption with its corresponding property.

🧠 Memory Trick

"Certain–Known, Add–Sum, Divide–Fractions, Proportion–Linear."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Fundamental Assumptions of LPP

12 Analytically identify the incorrect statement regarding the divisibility assumption:

A It implies decision variables are continuous.

B It restricts solutions to integer values only.

C Fractional outputs are allowed.

D It applies to both objective function and constraints.

💡 Short Explanation

Divisibility allows fractional values. Decision variables are continuous. Integer-only restrictions belong to Integer Programming.

✅ Correct Answer Explanation

The divisibility (continuity) assumption states that decision variables may take any real (fractional or integer) values, provided they satisfy all constraints. Option A is correct because divisibility implies continuity. Option B is incorrect because restricting variables to integers contradicts the divisibility assumption. Option C is correct because fractional outputs are permitted. Option D is acceptable because the assumption underlies the formulation of the linear objective function and constraints by allowing continuous decision variables throughout the model. Therefore, Option B is the correct answer.

❓ Why Other Options Are Incorrect

Option A) It implies decision variables are continuous. → This is the correct meaning of the divisibility assumption.
Option C) Fractional outputs are allowed. → Standard LPP permits fractional solutions.
Option D) It applies to both objective function and constraints. → The continuity of decision variables is assumed throughout the LPP model.

🎯 Strategy

used

Elimination

Application:

Recall the definition of the divisibility assumption and eliminate statements consistent with continuous decision variables.

Final Logic:

Divisibility allows fractional values, so integer-only solutions are incorrect.

🧠 Memory Trick

"Divisibility = Not Integers Only."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Divisibility (Continuity) Assumption

13 If the objective function is:
Z = 30x + 20y,
then doubling the output of x results in:

A Exponential increase in profit

B Shift in constraint lines

C No effect on profit

D Doubling of profit contribution from x

💡 Short Explanation

Profit contribution is proportional to output. Doubling x doubles 30x. This illustrates the proportionality assumption.

✅ Correct Answer Explanation

The objective function is: Z = 30x + 20y The contribution of x to the objective function is 30x. If x is doubled, then: 30(2x) = 60x Thus, the contribution from x doubles while the contribution from y remains unchanged. This demonstrates the proportionality assumption, which states that contributions change directly in proportion to activity levels. Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A) Exponential increase in profit → The increase is linear, not exponential.
Option B) Shift in constraint lines → Changing x does not alter the constraints.
Option C) No effect on profit → Profit clearly increases as x increases.

🎯 Strategy

used

Substitution

Application:

Replace x with 2x in the objective function and compare the contribution.

Final Logic:

Doubling x doubles its profit contribution.

🧠 Memory Trick

"Double x = Double Profit from x."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Proportionality Assumption

14 Maintaining a constant ratio between activity level and resource consumption is represented graphically by:

A A linear straight line

B A quadratic curve

C A sine wave

D A logarithmic curve

💡 Short Explanation

Constant ratios indicate proportionality. Proportional relationships produce straight lines. Linear Programming is based on linear relationships.

✅ Correct Answer Explanation

The proportionality assumption requires that resource consumption changes directly with the activity level. A direct proportional relationship is represented mathematically by a linear equation, whose graph is a straight line. Quadratic, logarithmic, and trigonometric curves do not maintain a constant rate of change and therefore do not satisfy the proportionality assumption. Hence, Option A is the correct answer.

❓ Why Other Options Are Incorrect

Option B) A quadratic curve → Represents a non-linear relationship.
Option C) A sine wave → Represents periodic variation, not proportionality.
Option D) A logarithmic curve → Represents a changing rate of increase rather than a constant ratio.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Associate the phrase constant ratio with linear relationship.

Final Logic:

Constant proportionality is represented by a straight line.

🧠 Memory Trick

"Constant Ratio = Straight Line."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Proportionality Assumption

15 Given the profit expression:
Z = 2x + 10y,
this relies on the assumption of:

A Non-negativity

B Additivity

C Iso-cost shifting

D Unbounded feasibility

💡 Short Explanation

Total profit equals the sum of individual profits. Each variable contributes independently. This illustrates the additivity assumption.

✅ Correct Answer Explanation

The objective function Z = 2x + 10y is obtained by adding the individual profit contributions: 2x from product x 10y from product y The total profit is simply their sum. This is the additivity assumption, which states that the total objective value equals the sum of the individual contributions without interaction terms. Therefore, Option B is correct.

❓ Why Other Options Are Incorrect

Option A) Non-negativity → This restricts decision variables to non-negative values and is unrelated to combining profits.
Option C) Iso-cost shifting → This is a graphical optimization technique, not an assumption.
Option D) Unbounded feasibility → This describes a feasible region, not the structure of the objective function.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Recognize that adding individual contributions indicates the additivity assumption.

Final Logic:

The objective function is the sum of individual profit contributions.

🧠 Memory Trick

"Additivity = Add Individual Profits."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Additivity Assumption

16 In transportation problems, additivity ensures that:

A Cost decreases continuously

B Distance remains constant

C Total cost equals sum of individual route costs

D Variables behave exponentially

💡 Short Explanation

Each transportation route contributes independently. Total transportation cost is obtained by adding individual route costs. This illustrates the additivity assumption.

✅ Correct Answer Explanation

The additivity assumption states that the total value of the objective function is the sum of the contributions made by individual decision variables. In a transportation problem, if: Route 1 has cost C₁, Route 2 has cost C₂, Route 3 has cost C₃, then the total transportation cost is: Total Cost = C₁ + C₂ + C₃ No interaction terms or multiplicative effects are involved. Therefore, Option C is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Cost decreases continuously → Additivity does not imply that cost decreases.
Option B) Distance remains constant → Distance is unrelated to the additivity assumption.
Option D) Variables behave exponentially → Linear Programming assumes linear relationships, not exponential ones.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Recognize that additivity means combining individual costs by simple addition.

Final Logic:

Total transportation cost equals the sum of the costs of all individual routes.

🧠 Memory Trick

"Additivity = Add Route Costs."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Additivity Assumption

17 If each unit requires 1.5 machine hours, continuity treats this as:

A Continuous real values

B Only integers

C Imaginary numbers

D Fixed constants

💡 Short Explanation

Machine-hour requirements may be fractional. Continuity allows real-valued quantities. Fractional values are acceptable in standard LPP.

✅ Correct Answer Explanation

The continuity (divisibility) assumption states that decision variables and related quantities may take real (including fractional) values. A requirement of 1.5 machine hours is therefore perfectly acceptable because it represents a continuous quantity. Thus, Option A is correct.

❓ Why Other Options Are Incorrect

Option B) Only integers → Standard LPP does not restrict variables to integers.
Option C) Imaginary numbers → Imaginary numbers have no role in Linear Programming.
Option D) Fixed constants → Although 1.5 is a coefficient, the question asks how continuity treats the value, namely as a continuous real quantity.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Identify that a fractional machine-hour requirement is permitted because of the continuity assumption.

Final Logic:

Fractional machine hours represent continuous real values.

🧠 Memory Trick

"1.5 Hours = Continuity."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Continuity (Divisibility) Assumption

18 Without continuity, solving the problem requires:

A Hyperbolic geometry

B Integer programming

C Removing constraints

D Ignoring objective function

💡 Short Explanation

Without continuity, fractional solutions are not allowed. Variables must take integer values. Such problems are solved using Integer Programming.

✅ Correct Answer Explanation

The continuity assumption permits fractional values of decision variables. If this assumption is removed, decision variables are restricted to integer values only. Problems with this restriction are solved using Integer Programming, which is an extension of Linear Programming. Therefore, Option B is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Hyperbolic geometry → This has no application in Linear Programming.
Option C) Removing constraints → Constraints remain an essential part of the optimization problem.
Option D) Ignoring objective function → Every optimization problem requires an objective function.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Recall that removing the continuity assumption leads to integer-only solutions.

Final Logic:

Without continuity, Integer Programming is required.

🧠 Memory Trick

"No Continuity = Integer Programming."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Continuity and Integer Programming

19 Which is NOT a core component of an LPP?

A Linear objective function

B Decision variables

C Hyperbolic roots

D Non-negative restrictions

💡 Short Explanation

LPP consists of decision variables, objective function, constraints, and non-negative restrictions. Hyperbolic roots are unrelated to Linear Programming. They are not part of LPP formulation.

✅ Correct Answer Explanation

A standard Linear Programming Problem consists of: Decision variables Linear objective function Linear constraints Non-negative restrictions Hyperbolic roots belong to a different area of mathematics and have no role in Linear Programming. Therefore, Option C is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Linear objective function → This is an essential component of every LPP.
Option B) Decision variables → They represent the unknown quantities to be optimized.
Option D) Non-negative restrictions → These ensure that decision variables do not take negative values.

🎯 Strategy

used

Odd One Out

Application:

Identify the option that does not belong to the standard components of an LPP.

Final Logic:

Hyperbolic roots are unrelated to Linear Programming.

🧠 Memory Trick

"Variables + Objective + Constraints = LPP."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Components of a Linear Programming Problem

20 Formulating an LPP involves structuring variables into:

A Iso-profit graphs only

B 3D polygons

C Corner point tables

D Linear equations and inequalities

💡 Short Explanation

Real-world situations are converted into mathematical models. The model consists of linear equations and inequalities. These define the objective function and constraints.

✅ Correct Answer Explanation

The first step in solving a Linear Programming Problem is to convert the practical situation into a mathematical model. This involves: Defining decision variables. Writing the objective function. Expressing the constraints as linear equations or inequalities. Therefore, Option D is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Iso-profit graphs only → Iso-profit graphs are used after formulation during graphical solution.
Option B) 3D polygons → Standard LPP formulation does not require three-dimensional polygons.
Option C) Corner point tables → Corner points are identified after graphing the constraints.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Recall that mathematical formulation converts a practical problem into linear equations and inequalities.

Final Logic:

An LPP is formulated using linear equations and inequalities.

🧠 Memory Trick

"Problem → Equations → Solution."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Mathematical Formulation of an LPP

CUET UG Applied Mathematics Booster Test 2 - Components, Assumptions, and Mathematical Formulation

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