The profit P, in millions of dollars, that a manufacturer makes is a function of the number N, in millions, of items produced in a year, and the formula is as follows. P = 10N − N2 − 7.14 A negative quantity for P represents a negative profit—that is, a loss—and the formula is valid up to a level of 10 million items produced. (a) Express using functional notation the profit at a production level of 4 million items per year. P (b) What is the loss at a production level of N = 0 million items? million dollars (c) Determine the two break-even points for this manufacturer — that is, the two production levels at which the profit is zero. (Round your answers to two decimal places.) million items (smaller value) million items (larger value) (d) Determine the production level that gives maximum profit. (Round your answer to two decimal places.) million items
The profit P, in millions of dollars, that a manufacturer makes is a function of the number N, in millions, of items produced in a year, and the formula is as follows. P = 10N − N2 − 7.14 A negative quantity for P represents a negative profit—that is, a loss—and the formula is valid up to a level of 10 million items produced. (a) Express using functional notation the profit at a production level of 4 million items per year. P (b) What is the loss at a production level of N = 0 million items? million dollars (c) Determine the two break-even points for this manufacturer — that is, the two production levels at which the profit is zero. (Round your answers to two decimal places.) million items (smaller value) million items (larger value) (d) Determine the production level that gives maximum profit. (Round your answer to two decimal places.) million items
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The profit P, in millions of dollars, that a manufacturer makes is a function of the number N, in millions, of items produced in a year, and the formula is as follows.
P = 10N − N2 − 7.14
A negative quantity for P represents a negative profit—that is, a loss—and the formula is valid up to a level of 10 million items produced.
(a) Express using functional notation the profit at a production level of 4 million items per year.
(b) What is the loss at a production level of N = 0 million items?
million dollars
(c) Determine the two break-even points for this manufacturer — that is, the two production levels at which the profit is zero. (Round your answers to two decimal places.)
million items (smaller value)
million items (larger value)
(d) Determine the production level that gives maximum profit. (Round your answer to two decimal places.)
million items
Determine the amount of the maximum profit. (Round your answer to two decimal places.)
million dollars
P
(b) What is the loss at a production level of N = 0 million items?
million dollars
(c) Determine the two break-even points for this manufacturer — that is, the two production levels at which the profit is zero. (Round your answers to two decimal places.)
million items (smaller value)
million items (larger value)
(d) Determine the production level that gives maximum profit. (Round your answer to two decimal places.)
million items
Determine the amount of the maximum profit. (Round your answer to two decimal places.)
million dollars
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