Summertime Tees sells two very popular styles of embroidered shirts in southern Florida: a tank top and a regular T-shirt. The cost of the tank top is $6, and the cost of the T-shirt is $8. The demand for these is sensitive to the price, and historical data indicate that the weekly demands are given by

X1 = 500 – 12P1

X2 = 400 – 15P2

Where

X1 = demand for tank top

P1 = price for tank top

X1 = demand for regular T-shirt

P2 = price for regular T-shirt

(a) Develop an equation for the total profit.

(b) The following nonlinear program. Use the profit function developed in part (a).

Maximize profit

Subject to X1 = 500 - 12P1

X2 = 400 - 15P2

P1 ≤ 20

P2 ≤ 25

X1, P1, X2, P2 ≥ 0