   Chapter 10, Problem 41RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Profit If in Problem 40 the mountain bikes cost the shop $680 each, at what selling price will MMRII’s profit be a maximum?Revenue MMR II Extreme Bike Shop sells 54 of its most popular mountain bikes per month at a price of$1540 each. Market research indicates that MMR II could sell one more of these bikes if the price were $10 lower. At what selling price will MMR II maximize the revenue from these bikes? To determine To calculate: The value of selling price at which MMR II will maximize the revenue for these bikes if the bike ship sells 54 of its most popular mountain bikes per month at a price of$1540 each and the market research indicates that it could sell one more of these bikes for each $20 price reduction and the bikes cost the shop$680.

Explanation

Given Information:

The provided information is the bike ship sells 54 of its most popular mountain bikes per month at a price of $1540 each and the market research indicates that it could sell one more of these bikes for each$20 price reduction and the bikes cost the shop $680. Formula Used: As per the product rule, if two functions are given in the form f(x).g(x), then the derivative is given as: ddx(f.g)=f.dgdx+g.dfdx The total revenue R is equal to R=pq, where p is the revenue per unit and q is the number of units. The revenue is maximized by finding the value of the variable at first derivative is equal to 0. Also checking by verifying that T(q)0 or not. Calculation: Consider the provided information, The bike ship sells 54 of its most popular mountain bikes per month at a price of$1540 each and the market research indicates that it could sell one more of these bikes for each $20 price reduction and the bikes cost the shop$680

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