The revenue and cost functions for a particular product are given below. The cost and revenue are given in dollars, and x represents the number of units .R(x) = -0.25x2 215xC(x) = 100x + 12918.75(a) How many items must be sold to maximize the revenue?(b) What is the maximum revenue?(c) Find the profit functionP(x)(d) How many items must be sold to maximize the profit?(e) What is the maximum profit?(f) At what production level(s) will the company break even on this product? (Enter your answers as a comma-separated list.)units

Question
Asked Oct 25, 2019
The revenue and cost functions for a particular product are given below. The cost and revenue are given in dollars, and x represents the number of units .
R(x) = -0.25x2 215x
C(x) = 100x + 12918.75
(a) How many items must be sold to maximize the revenue?
(b) What is the maximum revenue?
(c) Find the profit function
P(x)
(d) How many items must be sold to maximize the profit?
(e) What is the maximum profit?
(f) At what production level(s) will the company break even on this product? (Enter your answers as a comma-separated list.)
units
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The revenue and cost functions for a particular product are given below. The cost and revenue are given in dollars, and x represents the number of units . R(x) = -0.25x2 215x C(x) = 100x + 12918.75 (a) How many items must be sold to maximize the revenue? (b) What is the maximum revenue? (c) Find the profit function P(x) (d) How many items must be sold to maximize the profit? (e) What is the maximum profit? (f) At what production level(s) will the company break even on this product? (Enter your answers as a comma-separated list.) units

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Expert Answer

Step 1

As per norms, the first three questions are answered. The problem concerns finding optimium (extreme) values of the given functions

Step 2

How to determine the local maxima and minima o...

Basic facts
1)Maximum or min imum values
of a function f(x) occur at points
a,where f(a)= 0
2)if f(a)<0, x= a is a local max imum
if f(a) 0, x= a is a local minimum
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Basic facts 1)Maximum or min imum values of a function f(x) occur at points a,where f(a)= 0 2)if f(a)<0, x= a is a local max imum if f(a) 0, x= a is a local minimum

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