Chapter 2.1, Problem 40E

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7th Edition

Stefan Waner + 1 other

ISBN: 9781337274203

Textbook Problem

**T-Shirt Profit** The latest demand equation for your Yoda vs. Alien T-shirts is given by

*q* is the number of shirts you can sell in one week if you charge $*x* per shirt. The Student Council charges you $400 per week for use of their facilities, and the T-shirts cost you $5 each. Find the weekly cost as a function of the unit price *x*. Hence, find the weekly profit as a function of *x*, and determine the unit price you should charge to obtain the largest possible weekly profit. What is the largest possible weekly profit?

To determine

**To calculate:** The weekly cost as a function of the unit price

Explanation

**Given Information:**

The provided linear demand equation is,

Where,

The student council charges

**Formula Used:**

The relationship between Revenue and price is,

The relationship between Revenue and profit is,

The standard parabolic function is,

Where, *a, b* and *c* are arbitrary constants.

If

And, the formula for *x-* coordinate of vertex is,

**Calculation:**

Consider the linear demand equation,

As the Student council charges

Therefore, the total cost is given by,

Now, substitute

Therefore, total weekly cost as a function of unit price

Now, the relationship between Revenue and Price is,

Substitute

Therefore, the total Revenue

Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10E

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