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Total cost of producing goods. See attached for full description.

4. The total cost of producing q units of product is given by C(q) = q^3 - 60q^2 +1400q + 1000 for 0 < q <= 50; the product sells for $788 per unit. What production level maximizes profit? Find the total cost, total revenue, and total profit at this production level. Graph the cost and revenue functions on the same axes, and label the production level at which profit is maximized, and the corresponding cost, revenue, and profit.

8. The total cost C(q) of producing q goods is given: C(q) = 0.01q^3 - 0.6q^2 + 13q.
(a) What is the fixed cost?
(b) What is the maximum profit if each item is sold for $7?
(c) Suppose exactly 34 goods are produced. They all sell when the price is $7 each, but for each $1 increase in price, 2 fewer goods are sold. Should the price be raised, and if so by how much.

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The solution explains how to find the maximum profit using the derivative.

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