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# A developer has recently purchased a laundromat and an adjacent factory. For years, the

## Problem 12 Chapter 4.5

Applied Calculus | 5th Edition

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Applied Calculus | 5th Edition

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Problem 12

A developer has recently purchased a laundromat and an adjacent factory. For years, the laundromat has taken pains to keep the smoke from the factory from soiling the air used by its clothes dryers. Now that the developer owns both the laundromat and the factory, she could install filters in the factorys smokestacks to reduce the emission of smoke, instead of merely protecting the laundromat from it. The cost of filters for the factory and the cost of protecting the laundromat against smoke depend on the number of filters used, as shown in the table. Number of filters Total cost of filters Total cost of protecting laundromat from smoke 0 \$0 \$127 1 \$5 \$63 2 \$11 \$31 3 \$18 \$15 4 \$26 \$6 5 \$35 \$3 6 \$45 \$0 7 \$56 \$0 (a) Make a table which shows, for each possible number of filters (0 through 7), the marginal cost of the filter, the average cost of the filters, and the marginal savings in protecting the laundromat from smoke. (b) Since the developer wishes to minimize the total costs to both her businesses, what should she do? Use the table from part (a) to explain your answer. (c) What should the developer do if, in addition to the cost of the filters, the filters must be mounted on a rack which costs \$100? (d) What should the developer do if the rack costs \$50?

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