Explanation Given Information: If a customer buys x copies, then he or she pays, $ 600 x . Also, it cost the company $ 9 , 000 to develop the program and $ 2 to manufacture each copy. Formula used: Steps to solve optimization problems: Step 1: Identify the unknowns with the aid of diagram. Step 2: Identify the objective function, the quantity to maximize or minimize. Step 3: Identify the constraint, the equations relating variables or inequalities expressing limitations on the value of the variables. Step 4: State the optimization problem Step 5: Eliminate the extra variables, solve the constraint for one unknown and substitute in the objective function. Step 6: Find the absolute maximum or absolute minimum of the objective function. Calculation: As it is provided that if a customer buys x copies, then he or she pays, $ 600 x So the revenue for each product is, R = 600 x Also, it cost the company $ 9 , 000 to develop the program and $ 2 to manufacture each copy. Thus, the cost of manufacturing x copies will be, C ( x ) = 9 , 000 + 2 x Thus, the total profit will be the difference of revenue and the cost, so, P ( x ) = R ( x ) − C ( x ) = 600 x − 9 , 000 + 2 x Now, the average profit per copy will be obtained by dividing the above expression by x as, P ( x ) x = 600 x x − 9 , 000 x + 2 P ¯ = 600 x − 1 / 2 − 9 , 000 x − 1 + 2 Now, since the average profit needs to be maximized, so P ¯ is the objective function

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 12.2, Problem 62E

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To calculate: The number of copies that the customer would have to buy for Feature Rich software’s average profit per copy to be maximized if a customer buys x copies, then he or she pays $600x. Also, it cost the company $9,000 to develop the program and $2 to manufacture each copy.

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Chapter 12.2, Problem 61E

Chapter 12.2, Problem 63E

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Chapter 12 Solutions

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The number of copies that the customer would have to buy for Feature Rich software’s average profit per copy to be maximized if a customer buys x copies, then he or she pays $ 600 x . Also, it cost the company $ 9 , 000 to develop the program and $ 2 to manufacture each copy.

Solution Summary: The author calculates the number of copies that a customer would have to buy for Feature Rich software's average profit per copy to be maximized.

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To calculate: The number of copies that the customer would have to buy for Feature Rich software’s average profit per copy to be maximized if a customer buys x copies, then he or she pays $600x. Also, it cost the company $9,000 to develop the program and $2 to manufacture each copy.

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Chapter 12 Solutions