10th Edition

ISBN: 9780136174318

Author: Demana

Publisher: PEARSON

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Expert Solution & Answer

Chapter 1.7, Problem 49E

Solution

a.

To find: The function y1=ux that models the cost of producing x unstrung rackets.

The function that models the cost of producing x unstrung rackets is y1=23x+125000 .

Given information:

The cost of making each unstrung racket is $23 and total of $125000 in fixed overhead costs.

Calculation:

Multiply the number of rackets with the price of each unstrung racket and add fixed overhead costs to get the function that models the cost of producing unstrung rackets as follows:

y1=Cost of x unstrung racket + fixed overhead=23⋅x+125000=23x+125000

Conclusion:

The function that models the cost of producing x unstrung rackets is y1=23x+125000 .

b.

To find: The function y2=sx that models the cost of producing x strung rackets.

The function that models the cost of producing x strung rackets is y2=31x+125000 .

Given information:

The cost of making each unstrung racket is $23 and total of $125000 in fixed overhead costs.

Calculation:

Multiply the number of rackets with the price of each strung racket and add fixed overhead costs to get the function that models the cost of producing unstrung rackets as follows:

y2=Cost of x strung racket + fixed overhead=23+8⋅x+125000=31x+125000

Conclusion:

The function that models the cost of producing x strung rackets is y2=31x+125000 .

c.

To find: The function y3=Rux that models the cost of producing x unstrung rackets.

The function modelling the revenue generated by selling x unstrung rackets is y3=56x

Given information:

The cost of making each unstrung racket is $23 and total of $125000 in fixed overhead costs.

The price of an unstrung racket is $56 and the price of a strung racket is $79.

Calculation:

The selling price of one unstrung racket is $56. So, the selling price of x unstrung rackets is 56x .

Therefore, the function modelling the revenue generated by selling x unstrung rackets is y3=56x .

Conclusion:

The revenue function is y3=56x .

d.

To find: The function y4=Rsx that models the cost of producing x strung rackets.

The function modelling the revenue generated by selling x strung rackets is y4=79x .

Given information:

The cost of making each unstrung racket is $23 and total of $125000 in fixed overhead costs.

The price of an unstrung racket is $56 and the price of a strung racket is $79.

Calculation:

The selling price of one unstrung racket is $79. So, the selling price of x strung rackets is 79x .

Therefore, the function modelling the revenue generated by selling x unstrung rackets is y4=79x .

Conclusion:

The revenue function is y4=79x .

e.

To graph: The functions y1,y2,y3 and y4 on the same window.

Given information:

The cost of making each unstrung racket is $23 and total of $125000 in fixed overhead costs.

The price of an unstrung racket is $56 and the price of a strung racket is $79.

Graph:

Use a graphing tool to draw the graph of the functions as shown below.

Interpretation:

Selling strung rackets generates more revenue than selling unstrung rackets.

f.

To write: whether the company should manufacture unstrung or strung rackets.

The company should manufacture strung rackets.

Given information:

The cost of making each unstrung racket is $23 and total of $125000 in fixed overhead costs.

The price of an unstrung racket is $56 and the price of a strung racket is $79.

Calculation:

Consider the graph drawn in part (e).

From the graph it can be observed that the revenue generated by selling strung rackets is more than revenue generated by unstrung rackets. Thus, it is recommended to manufacture strung rackets.

Conclusion:

Selling strung rackets generates more revenue than selling unstrung rackets.

Chapter 1.7, Problem 48E

Chapter 1.7, Problem 50E

Chapter 1 Solutions

PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)

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Prob. 7QR Ch. 1.4 - Prob. 8QR Ch. 1.4 - Prob. 9QR Ch. 1.4 - Prob. 10QR Ch. 1.4 - In Exercises 14 find formulas for the functions...Ch. 1.4 - In Exercises 14 find formulas for the functions...Ch. 1.4 - Prob. 3E Ch. 1.4 - Prob. 4E Ch. 1.4 - Prob. 5E Ch. 1.4 - Prob. 6E Ch. 1.4 - Prob. 7E Ch. 1.4 - Prob. 8E Ch. 1.4 - Prob. 9E Ch. 1.4 - Prob. 10E Ch. 1.4 - Prob. 11E Ch. 1.4 - Prob. 12E Ch. 1.4 - Prob. 13E Ch. 1.4 - Prob. 14E Ch. 1.4 - Prob. 15E Ch. 1.4 - Prob. 16E Ch. 1.4 - Prob. 17E Ch. 1.4 - Prob. 18E Ch. 1.4 - Prob. 19E Ch. 1.4 - Prob. 20E Ch. 1.4 - Prob. 21E Ch. 1.4 - Prob. 22E Ch. 1.4 - Prob. 23E Ch. 1.4 - Prob. 24E Ch. 1.4 - Prob. 25E Ch. 1.4 - Prob. 26E Ch. 1.4 - Prob. 27E Ch. 1.4 - Prob. 28E Ch. 1.4 - Prob. 29E Ch. 1.4 - Prob. 30E Ch. 1.4 - Prob. 31E Ch. 1.4 - Prob. 32E Ch. 1.4 - Prob. 33E Ch. 1.4 - Prob. 34E Ch. 1.4 - Prob. 35E Ch. 1.4 - Prob. 36E Ch. 1.4 - Prob. 37E Ch. 1.4 - Prob. 38E Ch. 1.4 - Prob. 39E Ch. 1.4 - Prob. 40E Ch. 1.4 - Prob. 41E Ch. 1.4 - Prob. 42E Ch. 1.4 - Prob. 43E Ch. 1.4 - 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Prob. 19RE Ch. 1 - Prob. 20RE Ch. 1 - Prob. 21RE Ch. 1 - Prob. 22RE Ch. 1 - Prob. 23RE Ch. 1 - Prob. 24RE Ch. 1 - Prob. 25RE Ch. 1 - Prob. 26RE Ch. 1 - Prob. 27RE Ch. 1 - Prob. 28RE Ch. 1 - Prob. 29RE Ch. 1 - Prob. 30RE Ch. 1 - Prob. 31RE Ch. 1 - Prob. 32RE Ch. 1 - Prob. 33RE Ch. 1 - Prob. 34RE Ch. 1 - Prob. 35RE Ch. 1 - Prob. 36RE Ch. 1 - Prob. 37RE Ch. 1 - Prob. 38RE Ch. 1 - Prob. 39RE Ch. 1 - Prob. 40RE Ch. 1 - Prob. 41RE Ch. 1 - Prob. 42RE Ch. 1 - Prob. 43RE Ch. 1 - Prob. 44RE Ch. 1 - Prob. 45RE Ch. 1 - Prob. 46RE Ch. 1 - Prob. 47RE Ch. 1 - Prob. 48RE Ch. 1 - Prob. 49RE Ch. 1 - Prob. 50RE Ch. 1 - Prob. 51RE Ch. 1 - Prob. 52RE Ch. 1 - Prob. 53RE Ch. 1 - Prob. 54RE Ch. 1 - Prob. 55RE Ch. 1 - Prob. 56RE Ch. 1 - Prob. 57RE Ch. 1 - Prob. 58RE Ch. 1 - Prob. 59RE Ch. 1 - Prob. 60RE Ch. 1 - In Exercises 5964, write the specified quantity as...Ch. 1 - Prob. 62RE Ch. 1 - Prob. 63RE Ch. 1 - Prob. 64RE Ch. 1 - Prob. 65RE Ch. 1 - Prob. 67RE Ch. 1 - Prob. 68RE

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Solution Summary: The author analyzes the function y_1=u(x), which models the cost of producing unstrung rackets.

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Chapter 1 Solutions