The following question relate to a community that is circular in nature with a one mile circumference. There are 81 people evenly distributed around the lake where the town is built. The travel cost is $10 per mile, a restaurant costs $100 to set up, and the cost per meal is $2. What is the rate at which transportation costs are falling when the optimal number of restaurants is reached? Round off small residuals to the nearest whole number.
What will be an ideal response?
Since the optimal number of restaurants is obviously 2 from the sketch graph, and since the first derivative of the transportation cost function is tL/2N2, the rate at which transportation costs are falling for the community is 101.
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