The Rockastic Sports Bar has just opened in the newly rebuilt Wingbolt Casino & Resort. As part of a promotional sale, the company has decided to sell Wingbolt jackets for patrons. It costs $20 to manufacture each jacket.  In the first days of selling the jackets, the manager has noticed that when she charges $60 a jacket, 70 patrons will buy the jacket. When she charges $100 for a jacket only 30 patrons bought jackets. Assume the number of patrons who buy jackets is a linear function of price. What should she charge to ensure a maximum profit?

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter4: Systems Of Linear Equations
Section4.4: Solve Systems Of Equations With Three Variables
Problem 4.72TI: The community college soccer team sold three kinds of tickets to its latest game. The adult tickets...
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The Rockastic Sports Bar has just opened in the newly rebuilt Wingbolt Casino & Resort. As part of a promotional sale, the company has decided to sell Wingbolt jackets for patrons. It costs $20 to manufacture each jacket. 

In the first days of selling the jackets, the manager has noticed that when she charges $60 a jacket, 70 patrons will buy the jacket. When she charges $100 for a jacket only 30 patrons bought jackets. Assume the number of patrons who buy jackets is a linear function of price. What should she charge to ensure a maximum profit?

Expert Solution
Step 1

When she charges $60 a jacket, 70 patrons will buy the jacket. When she charges $100 for a jacket only 30 patrons bought jackets

Two coordinates are (60,70) and (100,30)

Let x=price , y= number of patrons

 

Step 2

Using the two coordinates we find the equation of the line.

Use the two point formula to find the equation of the line joining (60,70) and (100,30).

Algebra homework question answer, step 2, image 1

 

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