Math 1400 - Quiz # 4
Fall 2011
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10
Q1: The total profit, in dollars, from the sale of gas grills is
A. Use the marginal profit to estimate the profit from the sale of the 101st grill.
Marginal profit is
. Therefore, the marginal profit gives us the rate at which the profit is
changing and is measured in dollars per grill.
. This means, at a sales level of 100 grills the profit is increasing at a rate
of $16/grill. Or, we can say that the profit from the sale of one more grill (i.e. from the sale of the 101st grill)
is approximately $16.
B. If
estimate the total profit from the sale of 103 grills.
In part A we found that
. Using differentials, we can approximate
i.e. using the marginal profit at a sales level of 100, we can project that the total profit from 101 grills is
$1516, from 102 grills is $1532 and from 103 grills is $1548 etc. The further out we go the less reliable
these numbers are, since the marginal profit is always changing. In fact, the total profit from the sale of 103
grills is
. So, our estimate of $1,548 is $0.18 too high.
C. Find the average profit function and the marginal average profit function.
D. If
and
, estimate the average profit from the sale of 103 grills.
See the rest of the solutions on the next page.