A merchant intends to produce specialty carpets in the shape of the region in Figure 18
Chapter 8, Problem 34(choose chapter or problem)
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 carpets area. Using numerical integration with a computer algebra system, find the whole number n for which the merchants profits are maximal. 1 0.5 y = 1 x n 0.5 1 A y x
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