B.1 Solve the following linear programming problem

graphically:

Maximize profit = 4X + 6Y

Subject to: X + 2Y 8

5X + 4Y 20

X, Y 0

The optimum solution is the point where profit will be maximum after solving theconstraints

To determine the optimum solution point, Overlap the feasible region of constraint A and Constraint B. The point of intersection

of constraint A and cosntraint B is the optimum solution point.

Constraint A

X + 2Y 8

Constraint B

5X + 4Y 20

From the above graph, optimum solution point is X = 1.33 and Y = 3.33

Substitute these values in the objective function

Maximize Profit = 4X + 6Y

Profit

= 4(1.33) + 6(3.33)

Profit

25.3

Thus, the maximum profit is $25.3