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 _____

Question

For linear programming problem, the objective function is $ z = px + qy $, $ p,q>0 $. If at the corner points $ (0,10) $ and $ (5,5) $, the value of $ z $ are 90 and 60 respectively, then the relation between $ p $ and $ q $ is _____

Answer 1

Step 1: Understanding the Concept:
The optimal value (minimum or maximum) of an objective function in a Linear Programming Problem (LPP) always occurs at one of the corner points of the feasible region.
Step 2: Formula Application:
Evaluate $z = 3x + 9y$ at each point: 1. At (0, 10): $z = 3(0) + 9(10) = 90$ 2. At (5, 5): $z = 3(5) + 9(5) = 15 + 45 = 60$ 3. At (15, 15): $z = 3(15) + 9(15) = 45 + 135 = 180$ 4. At (0, 20): $z = 3(0) + 9(20) = 180$
Step 3: Explanation:
Comparing the values: 90, 60, 180, and 180. The smallest value is 60.
Step 4: Final Answer:
The minimum value is 60.

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 _____

Show Hint

The Correct Option is D

Solution and Explanation

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