Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,040 million units at a selling price of $p per unit. Assume a manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.] Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints. P(p) = ____ Find P′(p). P′(p) = ____ What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.) p = $____ What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.) $ ____ million
Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,040 million units at a selling price of $p per unit. Assume a manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.] Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints. P(p) = ____ Find P′(p). P′(p) = ____ What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.) p = $____ What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.) $ ____ million
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Worldwide annual sales of a device in 2012–2013 were approximately
manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.]
q = −6p + 3,040
million units at a selling price of $p per unit. Assume a Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints.
P(p) = ____
Find
P′(p).
P′(p) = ____
What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.)
p = $____
What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.)
$ ____ million
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