CBSE Class 12 Mathematics Linear Programming Assignment Set 04

Practice Questions with Answers

Question 1. What is the first step in formulating an LPP?
Answer:
Define the decision variables

Question 2. Shade the feasible region represented by the inequation system x + y ≤ 13, y ≤ 6, x ≥ 0, y ≥ 0.
Answer:
Bounded in first quadrant

Question 3. Consider the following LPP:
Maximise: Z = 12x + 10y
Subject to: 4x + 3y ≤ 480
2x + 3y ≤ 360
Determine the point at which the value of Z will be maximum.
Answer:
(60, 80)

Question 4. Determine the feasible region represented by the inequalities x ≤ 2 and y > 2.
Answer:
The feasible region is unbounded: it consists of all points to the left of (or on) the line x = 2 and above the line y = 2.

Question 5. Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy, where p, q > 0. Find the condition on p and q, so that the minimum of Z occurs at (3, 0) and (1, 1).
Answer:
\( p = \frac{q}{2} \)

Question 6. Determine the point at which the maximum value of x + y, subject to the constraints x + 2y ≤ 70, 2x + y ≤ 95, x, y ≥ 0 is obtained.
Answer:
(40, 15)

Question 7. In LPP, what is the nature of the objective function?
Answer:
Linear

Question 8. Find the minimum value of \( z = 2x_1 + 3x_2 \) subject to the constraints \( 2x_1 + 7x_2 \geq 22 \), \( x_1 + x_2 \geq 6 \), \( 5x_1 + x_2 \geq 10 \) and \( x_1, x_2 \geq 0 \).
Answer:
14

Question 9. In LPP, if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then where will Z have the maximum value?
Answer:
Every point of the line segment joining the two corner points.

Question 10. What is the objective of linear programming for an objective function?
Answer:
Maximize or Minimize