A company estimates that the initial cost of producing a commodity would be $680: The additional cost of manufacturing each item can be modeled by the function $m ( x ) = 3 x + 0.01 x ^ { 2 }$ , where x is the number of items produced and m is the manufacturing cost, in dollars. A market survey indicates the demand function can be estimated by $p ( x ) = 12 - 0.002 x$ .(a) Find the production level that maximizes profit. What is the maximum profit?
(b) What should the selling price be to maximize the profit?

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The Answer of A company estimates that the initial cost of producing a commodity would be $680: The additional cost of manufacturing each item can be modeled by the function $m ( x ) = 3 x + 0.01 x ^ { 2 }$ , where x is the number of items produced and m is the manufacturing cost, in dollars. A market survey indicates the demand function can be estimated by $p ( x ) = 12 - 0.002 x$ .(a) Find the production level that maximizes profit. What is the maximum profit?
(b) What should the selling price be to maximize the profit?

A Company Estimates That the Initial Cost of Producing a Commodity