A Port Authority Is in the Process of Deciding the Optimal

question 24

Essay

A port authority is in the process of deciding the optimal depth (in feet) of a harbor dredging project. Both commercial shippers and pleasure boaters use the harbor. The total cost of dredging the harbor (in hundreds of thousand dollars) is C = 2F + .25F², where F is harbor depth in feet. The total benefits to commercial shippers and pleasure boaters are: B_CS = 18F - .5F² and B_PB = 8F - .25F², respectively.
(a) Determine the optimal harbor depth.
(b) Comment on the following statement: “If the cost of dredging the harbor was zero, we could have, of course, dredged the harbor 20 or even 25 feet deep.”

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