A Mr. Peterson wants to sell cheese. After a fixed set-up cost of $250,
he can produce the cheese at a cost of $9 per kilogram. He is able to
produce up to 400kg,but he plans to take advance orders and
produce only what he can sell. His market research suggests that the
amount he would be able to sell depends on the price in the following
way: the mount decreases proportionally with the price; if he
charged $20 per kg he would not sell any, and if the cheese was free
he would ‘sell’ the maximum 400kg that he could produce. What price per kilogram should the farmer set in order to maximize his
profit?
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