T-Shirts R Us produces short-sleeved t-shirts, using domestic cotton and long-sleeved t-shirts from the same cotton. Although domestic cotton was readily available in the past, recently it has been much more difficult to obtain. Consultation with the plant managers of the two lines has resulted in the following production functions for shits and cotton usage in the two products:

Short Sleeve S = 3C_S- .004C_S²

Long Sleeve L = 12C_L- .02C_L²

Where S = units of short-sleeved shirts, L = units of long-sleeved shirts, C_S= cotton used in short-sleeved shirts and C_L= cotton used in long-sleeved shirts.

Short-sleeved shirts can be sold at a profit of $7 per unit, and long-sleeved shirts can be sold at a profit of $13 each.T-Shirts R Us has 3200 units of cotton available. How should it be allocated? Explain.