A developer has purchased a laundromat and an adjacent factory. To keep smoke, which ruins the clothes, out of the dryers the developer can protect the laundromat or install filters on the factory’s smokestacks. The daily 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 the table.
(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) What should the developer do to minimize total costs to the two businesses? 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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Number of filters 0 1 2 3 4 5 6 7 Total cost of filters $0 $5 $11 $18 $26 $35 $45 $56 Total cost of protecting laundromat from smoke $127 $63 $31 $15 $6 $3 $0 $0