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Unformatted text preview: , we know that
. But in order to keep
, we must have
. Therefore, the domain is
.
(B) Find the Revenue function
. (It should be a function of just the variable , no .)
Solution:
.
(C) If the goal is to maximize the daily Revenue, how many hats should be made each day, and what should be
the selling price (in dollars) for each hat? Show all details clearly.
Solution:
is a continuous function defined on a closed interval
. So the closed interval
method can be used to find the absolute max. We need to find the critical values of the function by
finding
and then setting
and solving for x. The derivative is
. When
we set
and solve for x, we find the critical value
. Finally, we make a list of the
important xvalues and find their corresponding
values.
important x values
(endpoint)
(critical)
(endpoint)
We see that the maximum Revenue occurs when
hats are made each day. The corresponding
selling price will be
dollars per hat.
(D) Find the Profit function
Solution: . (It should be a function of the variable .)
. (E) If the goal is to maximize the daily Profit, how many hats should be made each day, and what should be the
selling price (in dollars) for each hat?
Solution: We use the closed interval method again. We find the critical values of the function by setting
and solving for x. The derivative is
. When we set
and solve for
x, we find the critical value
. Finally, we make a list of the important xvalues and find their
corresponding
values.
important x values
(endpoint)
(The company is losing $7 per day!!)
(critical)
(endpoint)
(losing money)
We see that the maximum Profit occurs when
hats are made each day. The corresponding selling
price will be
dollars per hat....
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This document was uploaded on 02/17/2014 for the course MATH 1350 at Ohio University Athens.
 Fall '12
 barsamnian
 Math, Algebra

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