Download M111_HW3 1. - Question Details HarMathAp9 2.3.015. [1081083

M111_HW3
1. - Question Details HarMathAp9 2.3.015. [1081083]
The total costs and total revenues for a company are represented by the equations shown below, where
x represents the number of production units. Find the break-even points. (Enter your answers as a
comma-separated list.)
C(x) = 4200 + 10x + x2
R(x) = 140x
x=1
units
2. - Question Details HarMathAp9 2.3.020. [1090100]
If the profit function for a firm is given by P(x) = −16200 + 270x − x2 and limitations on space require that
production is less than 100 units, find the break-even points, where x represents the number of
production units. (Enter your answers as a comma-separated list.)
x=1
units
3. - Question Details HarMathAp9 2.3.023. [1081088]
market, the demand for a product is p = 190 − 0.20x and the revenue function is R = px, where x is the
number of units sold, what price will maximize revenue? (Round your answer to the nearest cent.)
$1
4. - Question Details HarMathAp9 2.3.034. [1096087]
The data in the table give sales revenues and costs and expenses for Continental Divide Mining for
various years.
Year
Sales Revenue
($ millions)
Costs and Expenses
($ millions)
1988
3.0845
2.4106
1989
3.4590
2.4412
1990
4.0626
2.6378
1991
4.0456
2.9447
1992
4.7614
2.5344
1993
4.7929
3.8171
1994
4.2227
4.2587
1995
4.7405
4.9869
1996
4.3686
4.9088
1997
4.8133
4.6771
1998
4.4200
4.9025
Assume that sales revenue for Continental Divide Mining can be described by the equation shown
below, where t is the number of years past 1982.
R(t) = –0.031t2 + 0.746t + 0.179
(a) Use the function to determine the year in which maximum revenue occurs. (Round your answer to
one decimal place.)
t=1
Find the maximum revenue the function predicts. (Round your answer to two decimal places.)
$2
millions
(b) Graph R(t) and the data points from the table.
5. - Question Details HarMathAp9 2.3.024. [1081122]
If, in a monopoly market, the demand for a product is p = 3400 − x and the revenue is R = px, where x is
the number of units sold, what price will maximize revenue? (Round your answer to the nearest cent.)
$1
6. - Question Details HarMathAp9 2.3.031. [1315886]
Suppose a company has fixed costs of $43,200 and variable costs of
1
3
x + 222 dollars per unit, where x is the total number of units produced. Suppose further that the selling
price of its product is 2046 −
2
3
x dollars per unit.
(a) Find the break-even points. (Enter your answers as a comma-separated list.)
x=1
(b) Find the maximum revenue. (Round your answer to the nearest cent.)
$2
(c) Form the profit function, P(x), from the cost and revenue functions. (Do not use commas in your
answer.)
P(x) =
3
Find maximum profit. (Round your answer to the nearest cent.)
$4
(d) What price will maximize the profit? (Round your answer to the nearest cent.)
$5
7. - Question Details HarMathAp9 2.3.018.MI. [1366138]
If total costs are C(x) = 300 + 260x and total revenues are R(x) = 300x − x2, find the break-even points,
where x represents the number of production units. (Enter your answers as a comma-separated list.)
x=1
units
8. - Question Details HarMathAp9 2.3.026.MI. [1365980]
The profit function for a firm making widgets is P(x) = 154x − x2 − 1600. Find the number of units at
which maximum profit is achieved.
x=1
units
Find the maximum profit.
$2
9. - Question Details HarMathAp9 2.3.032. [1315846]
Suppose a company has fixed costs of $2100 and variable costs of
3
4
x + 1600 dollars per unit, where x is the total number of units produced. Suppose further that the selling
price of its product is 1700 −
1
4
x dollars per unit.
(a) Find the break-even points. (Enter your answers as a comma-separated list.)
x=1
(b) Find the maximum revenue. (Round your answer to the nearest cent)
$2
(c) Form the profit function, P(x), from the cost and revenue functions. (Do not use commas in your
answer.)
P(x) =
3
Find maximum profit. (Round your answer to the nearest cent.)
$4
(d) What price will maximize the profit? (Round your answer to the nearest cent.)
$5
10. - Question Details HarMathAp9 2.2.044. [1272952]
Question part
The owner of a skating rink rents the rink for parties at $1080 if 60 or fewer skaters attend, so that the
cost per person is $18 if 60 attend. For each 5 skaters above 60, she reduces the price per skater by $.50.
(a) Construct a table that gives the revenue generated if 60, 70, and 80 skaters attend.
Price
No. of skaters Total Revenue
1
2
$3
4
5
$6
7
8
$9
(b) Does the owner's revenue from the rental of the rink increase or decrease as the number of skaters
increases from 60 to 80?
10
The revenue increases.
The revenue decreases.
(c) Enter the equation that describes the revenue for parties where x is the number of each additional 5
skaters more than 60.
R(x) =
11
(d) Find the number of skaters that will maximize the revenue.
12
skaters
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