must be in QM FOR EXCEL PROGRAM 1 A phosphate manufacturer p

must be in QM FOR EXCEL PROGRAM

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 800 kg. 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.

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

Solution

Let the number of Grade A Phosphate be x

Let the number of Grade B Phosphate be y

Let the number of Grade C Phosphate be z

Constraints:

4x + 4y + 5z <= 80 (labor hours constraint)

200x + 300y + 300z <= 6000 (Raw material 1 constraint)

600x + 400y + 500z <= 5000 (Raw material 2 constraints)

Necessary constraints x>=0,y>=0,z>=0

Profit Function: Z = 40x + 50y + 60z

The maxima exists at y=25/2 or 12.5Kg

Maximum Profit = 25/2 * 50 = 625$