Question

Consider the following LPP: Maximise $Z = 9x + 3y$ Subject to the constraints: $x + 3y \leq 60, \quad x - y \leq 0, \quad x \geq 0, \quad y \geq 0$ If $x = A, y = B$ is the optimum solution of the given LPP, then the value of $A + B$ is:

• A. 15
• B. 30
• C. 48
• D. 61

Answer 1

Answer: (B)

30

Answer 2

Plot the constraints and find the feasible region. The corner points of the feasible region are determined by the intersection of the following lines:

$x + 3y = 60, \quad x - y = 0, \quad x = 0, \quad y = 0.$

The corner points are $(0, 0), (0, 20), (15, 15)$. Evaluate $Z = 9x + 3y$ at these points:

$Z(0, 0) = 0, \quad Z(0, 20) = 60, \quad Z(15, 15) = 135.$

The maximum occurs at $(15, 15)$, so $A = 15, B = 15$, and:

$A + B = 15 + 15 = 30.$