A textile company in China is deciding whether or not they should specialize in jeans or t-shirts in order to maximize profit. It can make 70 HKD with one pair of jeans and 50 HKD with a teeshirt.

Each pair of jeans needs 3 hours of manufacturing time and 2 hours of dyeing, whereas for t-shirts, this time is 4 hours and 1 hour, respectively. The company has only 2,400 hours of manufacturing time and 1,000 hours of dyeing available daily.

There are other constraints the company needs to consider before deciding the perfect allocation.

It knows that the market cannot absorb more than 450 tee-shirts per day. Also, for contractual reasons, it needs to have a daily output of at least 100 pairs of jeans.

Determine:

a. The liner programming model

b. The optimal combination of t-shirts and jeans that maximizes the profit

c. A graphical solution

d. A computer solution

 LO.1