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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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