Question

2. Placid company makes 3 production components A, B, C using 3 machines Cutting, Polishing and     Packaging whose allocated and available hours are not more than 96hrs, 40hrs and 60hrs respectively. Product A spends 6 hours on cutting machine, 2 hours on polishing and 5 hours on packaging machine. Product B goes through 8 hours of cutting, 1 hour of polishing and 3 hours of packaging. Product C takes 4 hours on cutting machine, 4 hours of polishing and 2 hours of packaging. Contribution margins for each component product are N2, N5 and N8.

Use the Simplex Algorithm to determine how many of each component the Placid Company will make to maximize contribution

Answer 1

$\text{Let }x_1 \text{ represents the number of A}$

$\text{Let }x_2 \text{ represents the number of B}$

$\text{Let }x_3 \text{ represents the number of C}$

The linear program is

$Maximize:z=2x_1+5x_2+8x_3\\Subject to:\\6x_1+8x_2+4x_3\le90\\2x_1+x_2+4x_3\le40\\5x_1+3x_2+2x_3\le60$

with all variables non-negative.