1) Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,070 million units at a selling price o

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1) Worldwide annual sales of a device in 2012–2013 were
approximately
q = −6p + 3,070
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:
2) Worldwide annual sales of a product in 2013–2017 were
projected to be approximately
q = −10p + 4,460
million units at a selling price
of $p per unit.
Find the function R for projected revenue, in
millions of dollars and in terms of p only,
subject to any constraints.
R(p) =
Find
R′(p).
R′(p) =
What selling price (in dollars) would have resulted in the
largest projected annual revenue?
p = $
What would have been the resulting projected annual revenue (in
millions of dollars)?
$ million: