Question

1. A phosphate manufacturer produces three grades of phosphate, A, B, and C, which yield profit of $40, $50, and $60 per kilogram, respectively. The products require the labor and materials per batch that are shown in the table. Each batch of Grade A phosphate yields 800kg of phosphate; each batch of Grade B phosphate yields 700kg of phosphate; and each batch of Grade C phosphate yields 800kg of phosphate.

	Grade	Grade	Grade	Available
	A	B	C	Resources
Labor hours	4	4	5	80 hr
Raw material #1	200	300	300	6,000 kg
Raw material #2	600	400	500	5,000 kg

Formulate as an LP problem to maximize profit. What mix of products would yield maximize profit? (Use excel solver to find the optimal solution).

Answer 1

Objective function

Maximize profit = 40(800)A + 50(700)B + 60(800)C

Constraints

Labor: 4A +4B +5C <= 80

Raw material #1: 200A + 300B +300C<=6,000

Raw material #2: 600A + 400B +500C<=5,000

The solution is:

A = 0

B = 0

C = 10

Z = 480000