SOLUTION: You are starting a T-shirt business. Your fixed costs are $5,000. It costs $11 to buy each shirt. you plan to sell the shirts for $16. Write the total cost function, revenue funct

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Question 156478: You are starting a T-shirt business. Your fixed costs are $5,000. It costs $11 to buy each shirt. you plan to sell the shirts for $16. Write the total cost function, revenue function, profit function. Find the break even point.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You are going to sell x shirts.

It costs you $5000 plus $11 for each shirt, so the cost function is:

C%28x%29=5000+%2B+11x

You are going to sell each shirt for $16, so the revenue function is:

R%28x%29=+16x

The profit is the difference between the revenue and the cost, so:

P%28x%29+=+R%28x%29+-+C%28x%29 or

P%28x%29+=+16x+-+%285000+%2B+11x%29
P%28x%29+=+5x+-+5000

You break even when your profit is zero, that is P%28x%29=0, so:

5x-5000=0
5x=5000
x=1000

Hence, you break even when you sell 1000 shirts.