A merchant intends to produce specialty carpets in the shape of the region in Figure 18, bounded by the axes and graph of y 1 x n (units in yards) Assume that material costs $50 yd 2 and that it costs 50L dollars to cut the carpet, where L is the length of the curved side of the carpet The carpet c...

The area of the carpet is x1 1 A x dx x 1 1 1 n 1 10 n 1 while ...

A merchant intends to produce specialty carpets in the shape of the region in Figure 18, bounded

Question:

A merchant intends to produce specialty carpets in the shape of the region in Figure 18, bounded by the axes and graph of y = 1 − xⁿ (units in yards). Assume that material costs $50/yd² and that it costs 50L dollars to cut the carpet, where L is the length of the curved side of the carpet. The carpet can be sold for 150A dollars, where A is the carpet’s area. Using numerical integration with a computer algebra system, find the whole number n for which the merchant’s profits are maximal.

1 0.5 y A 0.5 y=1-x" 1