Mathematics Homework Help

I’m working on a Statistics question and need guidance to help me study.

Case Study 1Angelita owns a small Native American gift shop in Arizona.  Recently, she acquired a large collection of hand-woven Navajo rugs from another shop owner who was retiring.  This owner told Angelita that she would sell about 40 rugs a month at $150/rug but only 20 rugs per month at $220/rug. 

1.   Assuming a linear relationship between the price per rug and the number of rugs sold, find the demand function ?=?(?).

2.   Angelita paid the other owner $80 per rug for the collection.  She calculates fixed costs by taking the same percentage of her average monthly costs to run the store as the percentage of display space needed by the product in question.  Her average monthly cost is $3000 and her total amount of display space is 1200 square feet.  The rug display uses 120 square feet of display space.  Find the cost function ?=?(?).

3.   Find the revenue function for Angelita’s rugs.  State the domain of the revenue function. How many rugs does Angelita need to sell for maximum revenue?

4.   Find the profit function for Angelita’s rugs.  State the domain of the profit function.  How many rugs does Angelita need to sell for maximum profit?  What is the maximum profit?

5.   Graph the cost and revenue functions on the same graph.  Determine the break-even point and interpret its meaning in the context of this problem.  How many rugs should be sold in order for Angelita to make money?