   Chapter 11.3, Problem 82E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Pricing Policy Let us turn Exercise 81 around a little: Dorothy Wagner is currently selling 20 “I ♥ Calculus” T-shirts per day, but sales are dropping at a rate of 3 per day. She is currently charging $7 per T-shirt, and she wishes to increase her daily revenue by$10 per day. At what rate should she increase the unit price to accomplish this (assuming that the price increase does not affect sales)?

To determine

To calculate: The rate by which Dorothy Wagner should increase the price per unit such that her daily revenue increases by $10 per day where daily sales of Dorothy Wagner’s 20 “I ♥? Calculus” T-shirts is dropping at a rate of 3 per day and she is currently charging$7 per T-shirt.

Explanation

Given Information:

The daily revenue increases by $10 per day where daily sales of Dorothy Wagner’s 20 “I ♥? Calculus” T-shirts is dropping at a rate of 3 per day and she is currently charging$7 per T-shirt.

Formula used:

Product rule of derivative of differentiable functions, f(x) and g(x) is

ddx[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)

Calculation:

Assume the function S(t) be the number of T-shirts sold in 1 day.

As 20 T-shirts are sold in 0th day.

So,

S(0)=20

And rate of number of T-shirt’s is decreasing by 3 per day

So,

S'(0)=3

Assume the function P(t) be the price of 1 T-shirt.

At 0th day the price was \$7 per T-shirt.

So,

P(0)=7

As, revenue R(t)=P(t)Q(t)

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