For a certain product, the price-demand function is p (x) = 400 − 0.1x. The variable costs are $225 per unit, and the fixed costs are $3000.
(a) Determine the linear cost function C.
(b) Determine the revenue function R.
(c) Determine the profit function P (x) = R (x) − C (x).
(d) Use the Zero command on your calculator to find the zeros of the profit function P. These are the break-even points.
(e) Find the vertex of the graph of the profit function P.
(f) Determine the demand level that yields the maximum profit and find the maximum profit.
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