Question

The coordinates of the corner points of the bounded feasible region are \( (0,10), (5,5), \\ (15,15), (0,20) \). The minimum of the objective function \( z = 3x + 9y \) is _____

• A. \( 180 \)
• B. \( 30 \)
• C. \( 90 \)
• D. \( 60 \)

Hint:

Always check all corner points in LPP — no shortcuts!

Answer 1

The Correct Option is D

Concept: In Linear Programming, optimum value occurs at corner points.
Step 1: Evaluate objective function. At \( (0,10) \): \[ z = 3(0) + 9(10) = 90 \] At \( (5,5) \): \[ z = 15 + 45 = 60 \] At \( (15,15) \): \[ z = 45 + 135 = 180 \] At \( (0,20) \): \[ z = 180 \]
Step 2: Minimum value = \( 60 \)