Question

Maximize P = 4x + 5y subject to 2x + y < 50 2 + 3y < 75 2 > 0 y > 0 Identify the feasible region as bounded or unbounded: List the corner points of the feasible region, separated by a comma and a space. If the region is unbounded, create appropriate ghost points and list those as well. For each corner point, list the value of the objective function at that point. The format should be (x1,y1) value 1, (x2,72) value2, et Identify the location and value of the maximum. The format should be (x,y) maximum_value.

Answer 1

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The value of the objective function at each of these extreme points is as follows: Extreme Point Objective function value Coordinates Lines through Extreme Point Z = 4x1 + 5x2 (x1-x2) + 0(0,0) 3 4 X120 X220 4(0) + 5(0) = 0 A(25,0) 4(25) + 5(0) = 100 B(15, 20) 1 - 2x1 + x2 > 50 4 - X220 1 - 2x1 + x2 s 50 2 X1 + 3x2 = 75 2 - X1 + 3x2 s 75 3 - X1 20 4(15) + 5(20) = 160 C C(0,25) 400) + 5(25) = 125 The maximum value of the objective function Z = 160 occurs at the extreme point (15, 20). Hence, the optimal solution to the given LP problem is: X1 = 15, X2 = 20 and max 2 = 160.

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