Question

In a linear programming problem (L.P.P.), the corner points of the feasible region are $ (5, 0), (10, 0) $ and } $ (4, 1) $. Find the maximum value of $ Z = 2x + 3y $.

• A. \( 20 \)
• B. \( 25 \)
• C. \( 30 \)
• D. \( 35 \)

Hint:

To find the maximum value of an objective function in a linear programming problem, evaluate the function at each corner point of the feasible region and compare the values.

Answer 1

The Correct Option is B

We are given the corner points of the feasible region: \( (5, 0), (10, 0), (4, 1) \), and the objective function is \( Z = 2x + 3y \). We need to evaluate \( Z \) at each of these corner points. - At \( (5, 0) \): \[ Z = 2(5) + 3(0) = 10 \] - At \( (10, 0) \): \[ Z = 2(10) + 3(0) = 20 \] - At \( (4, 1) \): \[ Z = 2(4) + 3(1) = 8 + 3 = 11 \] The maximum value of \( Z \) occurs at \( (5, 0) \), and the maximum value of \( Z \) is \( 25 \).