=10-31 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 X P X P 1 1 2 2 500 12 400 15

= −

= −

where X

P X

1=

=

=

demand for tank top price for tank top demand for r 1

2 egular T-shirt price for regular T-shirt P2 =

(a) Develop an equation for the total profit.

(b) Use Excel to find the optimal solution to the following nonlinear program. Use the profit function developed in part (a).

Maximize profit subject to X P 1 X P P

P X

= −

= −

≤

≤

500 12 400 15 20 25 1

2 2 1

2 1 1 2 2 ,P , , X P ≥ 0