Question

If objective function for LPP is\( z=5x+7y \)and corner points of feasible region are\( (0, 0) (7, 0) (3, 4)\) and\( (0, 2) \)then maximum value of \( z \) occurs at :
\((A) (0,0)\)
\((B) (7,0)\)
\((C) (3,4)\)
\((D) (0,2)\)
\((E) (4,3) \)
Choose the correct answer from the options given below:

• A. (A) and (E) Only
• B. (C) Only
• C. (C) and (B) Only
• D. (C), (D), (B) Only

Answer 1

The Correct Option is B

The objective function for the Linear Programming Problem (LPP) is given by \( z=5x+7y \). We need to find where the maximum value of \( z \) occurs among the provided corner points of the feasible region: \( (0,0) \), \( (7,0) \), \( (3,4) \), and \( (0,2) \). To solve this, we calculate the value of \( z \) at each corner point:

• At \( (0,0) \), \( z = 5(0) + 7(0) = 0 \).
• At \( (7,0) \), \( z = 5(7) + 7(0) = 35 \).
• At \( (3,4) \), \( z = 5(3) + 7(4) = 15 + 28 = 43 \).
• At \( (0,2) \), \( z = 5(0) + 7(2) = 14 \).

The highest value of \( z \) is 43, which occurs at the point \( (3,4) \). Thus, the correct answer is:

(C) Only