# College Algebra

posted by
**Michael** on
.

Can you please help me solve this word problem?

Your boss has asked you to come up with a price model for one of the cell phone models that your company produces. In the model, costs and length of service are directly related. You are also asked to examine the profit formula based on selling a certain number of the phones to determine profitability based on how many are sold.

1. Suppose a cell phone service costs $45 per month, along with a $60 activation fee.

1. Write a cost equation that relates the number of months of service and the total cost for that time of service. (Hint: Let t = the number of months of service and c = the total cost.)

2. Use the cost equation to determine the number of months of service for a cost of $1,185.

2. Your company has determined that the profit equation (in thousands of dollars) of producing x thousand smartphones is as follows:

Profit = –x2 + 110x – 1,000

(If the number of smartphones is 40,000, for example, then x = 40). The break-even point is the number of smartphones sold and produced that would result in a profit of zero.

Use your preferred method for solving the quadratic equation to determine the break-even point.