A textile company produces two different types of shirts made of cotton. Standard shirts require 3 pounds of cotton per yard, whereas deluxe shirts require 6 pounds of cotton per yard. A yard of deluxe shirt requires 2.1 hours of processing time, and a yard of standard shirt needs just 1.9 hours. We consider that the demand for standard shirts is unlimited (i.e., we will sell all we can produce); however, the demand for deluxe shirts is limited to 400 yards per month. 2 The company currently has 4,300 pounds of cotton and 2,100 hours of processing time available to be used in the upcoming month. Their marginal profits per product are $1.80 per yard of standard shirt and $2.75 per yard of deluxe shirt. This textile company aims at selecting a production level that maximizes profits and, to that end, they use the following LP model, which they solve in Excel:

x1 = no. of yards of standard shirt

x2 = no. of yards of deluxe shirt

maximize Z = $1.80x1 + 2.75x2

subject to

3.0x1 + 6x2 ? 4,300

2.1x1 + 1.9x2 ? 2,100

x2 ? 400

x1, x2 ? 0

The computer solution is shown below: