A manufacturer of widgets has fixed costs of $650 per month, and the variable cost is $66 per thousand widgets (so it costs $66 to produce 1 thousand widgets). Let N be the number, in thousands, of widgets produced in a month. (a) Find a formula for the manufacturer's total cost C as a function of N. C(N) =
A manufacturer of widgets has fixed costs of $650 per month, and the variable cost is $66 per thousand widgets (so it costs $66 to produce 1 thousand widgets). Let N be the number, in thousands, of widgets produced in a month. (a) Find a formula for the manufacturer's total cost C as a function of N. C(N) =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 79RE
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Question
A manufacturer of widgets has fixed costs of $650 per month, and the variable cost is $66 per thousand widgets (so it costs $66 to produce 1 thousand widgets). Let N be the number, in thousands, of widgets produced in a month.
(a) Find a formula for the manufacturer's total cost C as a function of N.
C(N) =
(b) The highest price p, in dollars per thousand widgets, at which N can be sold is given by the formula
R(N) =
(c) Use your answers to parts (a) and (b) to find a formula for the profit P of this manufacturer as a function of N.
P(N) =
(d) Use your formula from part (c) to determine the two break-even points for this manufacturer. Assume that the manufacturer can produce at most 500 thousand widgets in a month. (Round your answers to two decimal places.)
C(N) =
(b) The highest price p, in dollars per thousand widgets, at which N can be sold is given by the formula
p = 75 − 0.02N.
Using this, find a formula for the total revenue R as a function of N.R(N) =
P(N) =
__________ thousand widgets per month (smaller value) |
__________ thousand widgets per month (larger value) |
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