10th Edition

ISBN: 9780136174318

Author: Demana

Publisher: PEARSON

Concept explainers

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

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Expert Solution & Answer

Chapter 1.7, Problem 47E

Solution

(a)

The equation models the costs of producing x pair of item-S.

The cost function model is Cx=30x+100,000 .

Given:

The annual cost C of making x pairs of items is $30 per pair of item and fixed amount of $100,000 .

Concept Used:

The cost function is made up of two quantity, one a variable quantity that depends on numbers of productions and other is constant, that is fixed.

Calculation:

If Cx be the cost function, then the annual costs of x pairs of items is $30 plus the fixed amount of $100,000 .

Thus, the equation models of the costs of producing x pair of item is:

Cx=30x+100,000 .

Conclusion:

The cost function model is Cx=30x+100,000 .

(b)

The equation models the revenue of selling x pair of item-S.

The equation models the revenue of selling x pair of item-S is Rx=50x .

Given:

The annual cost C of making x pairs of items is $30 per pair of item and fixed amount of $100,000 . The item is sold at price of $50 per item.

Concept Used:

The revenue is the amount generated by selling the item.

Calculation:

The item-C is sold at $50 . So the revenue generated by selling x numbers of items is 50x .

Hence, the equation models the revenue of selling x pair of item-S is:

Rx=50x , where Rx is revenue function.

Conclusion:

The equation models the revenue of selling x pair of item-S is Rx=50x .

(c)

The numbers of pairs to be produce and sold in order to break even.

The graph of equation model cost and revenue intersecting at break-even.

Given:

The annual cost C of making x pairs of items is $30 per pair of item and fixed amount of $100,000 . The item is sold at price of $50 per item.

Concept Used:

The break-even point arrives when cost and revenue are equal.

Calculation:

The cost and revenue function for x pairs of items is Cx=30x+100,000 and Rx=50x respectively.

If x is the numbers of pairs in order to break even, then Cx=Rx or 30x+100,000=50x .

Solve 30x+100,000=50x for x .

30x+100,000=50x100,000=50x−30x100,000=20x100,00020=xx=5,000

Hence, the numbers of pairs to be produce and sold in order to break even is 5,000 .

Conclusion:

The numbers of pairs to be produce and sold in order to break even is 5,000 .

(d)

The graph of equation that models the cost and revenue and interprets the break-even point.

The numbers of pairs to be produce and sold in order to break even is 5,000 .

Given:

The annual cost C of making x pairs of items is $30 per pair of item and fixed amount of $100,000 . The item is sold at price of $50 per item.

Concept Used:

Plot the points on graph obtained by choosing different values of x and join the points.

Calculation:

The cost function is Cx=30x+100,000 and the revenue function is Rx=50x .

To graph the functions, compute the values for different values of x :

The points are plotted as follows:

Interpretation:

The graph of two equation of cost and revenue model intersect at 5000, 25000 . Means the value of x and the function is same at the point. So cost and revenue of x=5,000 units is same and is equal to $25,000 . Hence the point of intersection gives the break even as calculated in part (c)

Conclusion:

The graph of equation model cost and revenue intersecting at break-even.

Chapter 1.7, Problem 46E

Chapter 1.7, Problem 48E

Chapter 1 Solutions

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

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

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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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Give...Ch. 1.5 - Prob. 15E Ch. 1.5 - Prob. 16E Ch. 1.5 - Prob. 17E Ch. 1.5 - Prob. 18E Ch. 1.5 - Prob. 19E Ch. 1.5 - Prob. 20E Ch. 1.5 - Prob. 21E Ch. 1.5 - Prob. 22E Ch. 1.5 - Prob. 23E Ch. 1.5 - Prob. 24E Ch. 1.5 - Prob. 25E Ch. 1.5 - Prob. 26E Ch. 1.5 - Prob. 27E Ch. 1.5 - Prob. 28E Ch. 1.5 - Prob. 29E Ch. 1.5 - Prob. 30E Ch. 1.5 - Prob. 31E Ch. 1.5 - Prob. 32E Ch. 1.5 - Prob. 33E Ch. 1.5 - Prob. 34E Ch. 1.5 - Prob. 35E Ch. 1.5 - Prob. 36E Ch. 1.5 - Prob. 37E Ch. 1.5 - Prob. 38E Ch. 1.5 - Prob. 39E Ch. 1.5 - Prob. 40E Ch. 1.5 - Prob. 41E Ch. 1.5 - Prob. 42E Ch. 1.5 - Prob. 43E Ch. 1.5 - Prob. 44E Ch. 1.5 - Prob. 45E Ch. 1.5 - Prob. 46E Ch. 1.5 - Prob. 47E Ch. 1.5 - Prob. 48E Ch. 1.5 - Prob. 49E Ch. 1.5 - Prob. 50E Ch. 1.5 - Prob. 51E Ch. 1.6 - Prob. 1QR Ch. 1.6 - Prob. 2QR Ch. 1.6 - Prob. 3QR Ch. 1.6 - Prob. 4QR Ch. 1.6 - Prob. 5QR Ch. 1.6 - Prob. 6QR Ch. 1.6 - Prob. 7QR Ch. 1.6 - Prob. 8QR Ch. 1.6 - Prob. 9QR Ch. 1.6 - Prob. 10QR Ch. 1.6 - Prob. 1E Ch. 1.6 - Prob. 2E Ch. 1.6 - Prob. 3E Ch. 1.6 - 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Solution Summary: The equation models the costs of producing x pair of item-S. The cost function model is C(x)=30x+100,000

Concept explainers

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Chapter 1 Solutions