Page 233 - How To Solve Word Problems In Calculus

the demand changing when the selling price is $1.25 and dropping at
the rate of 15 cents per month?
3. A yacht manufacturer finds that his profit in dollars for
manufacturing and selling x yachts is given by the function
2
2
p(x) = (x + 2x) .If he can produce 4 yachts per month, at what
rate is his profit increasing at the end of 6 months?
4. A manufacturer’s total monthly revenue when x units are produced
2
and sold is R(x) = 300x + 0.075x .
(a) Use marginal analysis to estimate the additional revenue
generated by the manufacture and sale of the 51st unit.
(b) Compute the actual revenue generated by the manufacture and
sale of the 51st unit.
5. The cost of manufacturing x units of a commodity is given by the
function C (x) = 50x + 400. x units are sold when the price per
unit is 500 − 2x dollars.Use marginal analysis to approximate the
profit or loss incurred in manufacturing and selling the 100th unit.
Compare this with the exact value.
6. When the price of a certain commodity is p dollars per unit, a
manufacturer will supply x thousand units where
√
2
x + 2x p − p = 25.If the price is increasing at the rate of $1 per
week, how fast is the supply changing when the price is $100 per unit?
7. A small shop sells teddy bears for $28 each.The daily cost to
produce x bears is determined by the function

2
3
C (x) = x − 6x + 13x + 15
Find the number of bears that should be produced and sold to
maximize daily profit.What is the maximum profit?
8. A toll road averages 300,000 cars a day when the toll is $2.00 per
car.A study has shown that for each 10-cent increase in the toll,
10,000 fewer cars will use the road each day.What toll will
maximize the revenue?
9. A company makes and sells cameras at a price of $60 each.Its daily
2
3
cost function is C (x) = 40 + 4x − 1.6x + 0.1x where x is the
number of cameras manufactured and sold in a day.If the company
can manufacture no more than 30 cameras per day, what level of
production will yield the maximum profit?
10. A publisher plans to sell 200,000 copies of a textbook in a year.If it
costs $3750 to set up a printing, $3 to print a book, and $600 to
store 1000 books for a year, what size printing runs will minimize
the publisher’s cost?

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