A garment factory produces shirts and pants for Kmart chain. The contract is such that

quality control is done before shipping and all products supplied to Kmart satisfying the

quality requirements would be accepted by the chain. The factory employs

$20$

$$workers

in the cutting department,

$50$

$$workers in the sewing department, and

$14$

$$workers in the

packaging department. The garment factory works

$8$

$$productive hours a day

$($

no idle

time during these

$8$

$$hours

$)$

$.$

$$There is a daily demand for at most

$180$

$$shirts$.$ The demand

for pants is unlimited. Each worker can participate only in one activity

$-$

$$the activity to

which they are assigned. The table below gives the time requirements

$($

in minutes

$)$

$$and

profit per unit for the two garments.

Amount

$($

minutes

$)$

$$per operation

Cutting Sewing Packaging Profit per unit

$($

$

$)$