Question

For an L.P.P. the objective function is Z = 4x + 3y and the feasible region determined by a set of constraints (linear inequations) is shown in the graph.

Which one of the following statements is true?

Options

• Maximum value of Z is at R.

• Maximum value of Z is at Q.

• Value of Z at R is less than the value at P.

• Value of Z at Q is less than the value at R.

Answer 1

Maximum value of Z is at Q.

Explanation:

Corner Points of Feasible Region	Value of z = (z = 4x + 3y)
O(0, 0)	Z = 4(0) + 3(0) = 0
P(0, 40)	Z = 4(0) + 3(40) = 120
Q(30, 20)	Z = 4(30) + 3(20) = 180 (Maximum)
R(40, 0)	Z = 4(40) + 3(0) = 160

Thus, Maximum value of z is at Q, which is 180.