Question

If the objective function for an LPP is \( z=3x-4y \) and corner points for bounded feasible region are \((5, 0) (6, 5) \)and \((4, 10)\), then:
(A) maximum value of \(z\) is \(2\)
(B)minimum value of\( z\) is \(2\)
(C) maximum value of \(z \)is at \((5, 0)\)
(D) no maximum value of\( z\)
(E)maximum value of \(z\) is \(15\)
Choose the correct answer from the options given below:

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

Answer 1

The Correct Option is D

The objective function given is \(z=3x-4y\). We need to evaluate this function at each corner point of the feasible region to determine the maximum and minimum values.
Let's calculate \(z\) at each corner point:

• At \((5,0)\): \(z=3(5)-4(0)=15\)
• At \((6,5)\): \(z=3(6)-4(5)=18-20=-2\)
• At \((4,10)\): \(z=3(4)-4(10)=12-40=-28\)

From these calculations, the maximum value of \(z\) is \(15\) at the point \((5,0)\). Therefore, the correct options are (C) and (E), which is "maximum value of \(z\) is at \((5,0)\)" and "maximum value of \(z\) is \(15\)".