Profit Analysis—Bobbleheads: The financial planning team at the Tesch Company determines that the profit function for producing and selling its Captain U.S. bobbleheads can be modeled by
P(x) = −0.001x2 + 8x − 4000 0 ≤ x ≤ 7000
where x represent the number of bobbleheads produced and sold and P(x) represents the monthly profit in dollars.
(a) Determine MP, the marginal profit function. Evaluate MP(3000) and interpret.
(b) If the Tesch Company is producing and selling 3000 bobbleheads per month, is profit increasing or decreasing?
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