Explain why the total revenue from the sale of x shirts at the price p(x) is R(x)=16x-0.005x^2 where Rx=dollar

Question

You have identified the following costs:
Heat Press: 612.50
Shirts in Bulk: 2.50
Transfers to press on shirts: 1.00

Write a function C(x), that gives the total cost of producing shirts: ?

Target Shirt sales, x | Price Per shirt P
500 = 13.5$
900 = 11.5$
1300 = 9.5$
1700=7.5$
2100= 5.5$
2500= 3.5$

Based on that info, write a function p(x) that gives the selling price per shirt that would enable you to sell x shirts during the semester. P(x)???

Explain why the total revenue from the sale of x shirts at a price p(x) dollars per shirt is given by R(x)=16x-.005x^2 where R(x) is in dollars

Since Profit = Revenue - Cost, wrie tthe function P(x), that gives the net profit from the sale of x shirts

Write an inequality for the following: How many t-shirts must you sell to make a profit?


Thank you anyone for any help/answers/advice that you may have to offer. I think I may have some of these answers but I doubt that they're right. Any help is appreciated.

Answer 1

C(x) = 612.50 +3.5x
p(x) = -x/200+16 = -.005x+16 = price per shirt
R(x) = xP(x) = -.005x^2+16x
P(x) = -.005x^2+16x -612.5-3.5x = -.005x^2 +12.5x -612.5
-.005x^2+16x-612.5>0 to make profit