Page 232 - How To Solve Word Problems In Calculus

the storage cost is $24 per tire per year. How many tires should
be ordered in each shipment in order to minimize the total
cost?
Solution
Let x = size of each shipment. In this problem
C(x) = H(x) + O(x). The price per tire ($75) has no bearing on
the solution (see note above). Assuming that the demand for
the product is uniform throughout the year, it follows that

x 4000
C(x) = 24 + 30
2 x
= 12x + 120,000x −1

C (x) = 12 − 120,000x −2

120,000
0 = 12 −
x 2
120,000
= 12
x 2

2
12x = 120,000
2
x = 10,000
x = 100

In order to minimize cost, the tires should be ordered in
40 shipments of 100 tires each.

Supplementary Problems

1. If a company invests x thousand dollars in advertising, the demand
2
for its product will be D(x) = 2000x + 900x + 60 items.Find the
rate of change in demand with respect to advertising dollars when
$1500 is spent on advertising.
2. A family’s demand x for gasoline at a selling price p is given by the
function
x = 2000 − 100p − 0.05p 2

where x is measured in gallons and p is in dollars.At what rate is
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