Department Directory | Highline College
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[pic] units
[pic][pic][pic]
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[pic] units
[pic][pic][pic]
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[pic]
[pic][pic]
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 | |Costs and Expenses |
| | |($ millions) | |($ 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[pic]
Find the maximum revenue the function predicts. (Round your answer to two decimal places.)
$ 2[pic] millions
(b) Graph R(t) and the data points from the table.
|[pic][pic][pic] |[pic][pic] |
|[pic][pic] |[pic][pic] |
[pic][pic]
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[pic]
[pic][pic][pic]
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[pic]
(b) Find the maximum revenue. (Round your answer to the nearest cent.)
$ 2[pic]
(c) Form the profit function, P(x), from the cost and revenue functions. (Do not use commas in your answer.)
P(x) =
3
[pic][pic][pic][pic]
Find maximum profit. (Round your answer to the nearest cent.)
$ 4[pic]
(d) What price will maximize the profit? (Round your answer to the nearest cent.)
$ 5[pic]
[pic][pic]
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[pic] units
[pic][pic][pic]
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[pic] units
Find the maximum profit.
$ 2[pic]
[pic][pic][pic]
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[pic]
(b) Find the maximum revenue. (Round your answer to the nearest cent)
$ 2[pic]
(c) Form the profit function, P(x), from the cost and revenue functions. (Do not use commas in your answer.)
P(x) =
3
[pic][pic][pic][pic]
Find maximum profit. (Round your answer to the nearest cent.)
$ 4[pic]
(d) What price will maximize the profit? (Round your answer to the nearest cent.)
$ 5[pic]
[pic][pic][pic]
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 $.50.
(a) Construct a table that gives the revenue generated if 60, 70, and 80 skaters attend.
| |Price |
| |No. of skaters |
| |Total Revenue |
| | |
| |1[pic] |
| |2[pic] |
| |$ 3[pic] |
| | |
| |4[pic] |
| |5[pic] |
| |$ 6[pic] |
| | |
| |7[pic] |
| |8[pic] |
| |$ 9[pic] |
| | |
(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? [pic]
10
[pic]The revenue increases. [pic]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
[pic][pic][pic][pic]
(d) Find the number of skaters that will maximize the revenue.
12[pic] skaters
[pic][pic]
[pic]
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