Question

(a) A company makes three products X, Y and Z out of three materials A, B and C. The three products use the three materials as shown in the table below
A B C
X 2 4 6
Y 4 2 2
Z 6 4 2
The unit profit contributions for the three products are shillings 6, 8 and 10 for products X, Y and Z respectively. The material amounts available for A, B and C are 20, 24 and 30 respectively. Use simplex method to determine the maximum profit and the product mix. (10 Marks

Answer 1

so you want to maximize p = 6x+8y+10z subject to
2x+4y+6z ≤ 20
4x+2y+4z ≤ 24
6x+2y+2z ≤ 30
So graph the region and evaluate p at each vertex, as usual