Fifth Avenue’s goal is to maximize monthly profit given the following decision variables:
x1 = number of all-silk ties produced per month
x2 = number polyester ties
x3 = number of blend 1 poly-cotton ties
x4 = number of blend 2 poly-cotton ties
To determine the objective function, we have to find the profit per ties for fifth avenue.
Variety of tie |
Selling price/tie |
Material required per tie |
Material cost per yard |
Cost per tie |
Profit per tie |
All silk |
6.70 |
.125 |
21 |
2.62 |
4.08 |
All polyester |
3.55 |
.08 |
6 |
0.48 |
3.07 |
Poly cotton blend 1 |
4.31 |
.05 .05 |
6 9 |
0.30 0.45 |
3.56 |
Poly cotton blend 1 |
4.81 |
.03 .07 |
6 9 |
0.18 0.63 |
4.00 |
Thus, LPP model for Fifth Avenue Industries will be:
Objective function
Maximize profit = $4.08x1 + $3.07x2 + $3.56x3 + $4.00x4
Subject to
0.125 x1 ? 1000 (yards of silk)
0.08 x2 + 0.05 x3 + 0.03 x4 ? 2,000 (yards of polyester)
0.05 x3 + 0.07 x4 ? 12500 (yards of cotton)
x1? 6,000 (contract minimum for silk)
x1 ? 7,000 (contract maximum)
x2 ? 10,000(contract minimum for all polyester)
x2 ? 14,000 (contract maximum)
x3 ? 13,000 (contract minimum for blend 1)
x3 ? 16,000 (contract maximum)
x4 ? 6,000 (contract minimum for blend 2)
x4 ? 8,500 (contract maximum)
X1 , x2 , x3, x4 ? 0
1. Fifth Avenue Industries, a nationally known manufacturer of menswear, produces four varieties of ties. One...