A manufacturer of machinery parts determines that q units of a partic- ular piece will be sold when the price is p = 110 -q dollars per unit. The total cost of producing those q units is C(q) dollars, where C(q) = q° – 25q² + 2q + 3000. %3D - (a) Express the profit derived from the sale of the machinery parts in terms of q. Determine the domain of the profit function. (b) For what value of q is profit maximized? (c) Find the consumer's surplus for the level of production qo that corresponds to maximum profit.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A manufacturer of machinery parts determines that q units of a partic-
110 -q dollars per unit. The total cost
of producing those q units is C(q) dollars, where C(q) = q° – 25q² + 2q + 3000.
ular piece will be sold when the price is p =
(a) Express the profit derived from the sale of the machinery parts in terms of q.
Determine the domain of the profit function.
(b) For what value of q is profit maximized?
(c) Find the consumer's surplus for the level of production qo that corresponds to
maximum profit.
Transcribed Image Text:A manufacturer of machinery parts determines that q units of a partic- 110 -q dollars per unit. The total cost of producing those q units is C(q) dollars, where C(q) = q° – 25q² + 2q + 3000. ular piece will be sold when the price is p = (a) Express the profit derived from the sale of the machinery parts in terms of q. Determine the domain of the profit function. (b) For what value of q is profit maximized? (c) Find the consumer's surplus for the level of production qo that corresponds to maximum profit.
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