Question

The vertices of a closed convex polygon representing the feasible region of the LPP with objective function \(z = 5x + 3y\) are \((0,0)\), \((3,1)\), \((1,3)\) and \((0,2)\). The maximum value of \(z\) is:

• A. 6
• B. 18
• C. 14
• D. 15

Hint:

Evaluate the objective function at all vertices of feasible region to find the maximum.

Answer 1

The Correct Option is B

Calculate \(z = 5x + 3y\) at each vertex: \[ z(0,0) = 5 \times 0 + 3 \times 0 = 0 \] \[ z(3,1) = 5 \times 3 + 3 \times 1 = 15 + 3 = 18 \] \[ z(1,3) = 5 \times 1 + 3 \times 3 = 5 + 9 = 14 \] \[ z(0,2) = 5 \times 0 + 3 \times 2 = 6 \] Maximum value is \(18\) at \((3,1)\).