Question

Graph the following LP problem and indicate the optimal solution point: Maximize profit= $3X + 2Y Subject to 2X+ Y ≤ 150 2X + 3Y ≤ 300 a) Does the optimal solution change if the profit per unit of X changes to $4.50? b ) What happens if the profit function should have been $3X + 3Y? I need help solving this problem using solver in excel

Answer 1

The intersection point is (37.5, 75)

The trapezium with corner points (0,0), (0,100), (37.5,75), (75,0) is the feasible region.

Let us replace the corner points in Objective function to find out optimal solution.

The objective function value at

(0,0) :0

(0,100): 200

(37.5,75):262.5

(75,0): 225

The optimal solution point is (37.5, 75) where profit is 262.5

If you perform the sensitive analysis of the equations, the result will be

		Final	Reduced	Objective	Allowable	Allowable
Variable		Value	Cost	Coefficient	Increase	Decrease
X		37.5	0	3	1	1.67
Y		75	0	2	2.5	0.5

From the table, we can easily interpret that the allowable coefficient increase to variable X is 1 and Y is 2.5

a. If per unit profit of X is change to 4.5, then the optimal solution point changes. We can substitute values and see that (75,0) gives maximum value of 337.5 to the profit

b. If profit equation become 3X+3Y, even then optimal point remains same as allowable increase of coefficient to Y is 2.5. We can substitute values and see that 337.5 is maximum at (37.5,75)