Question

the function p (x) = 15x - 2,500 models the net profit on sales of a school logo T-shirt, where p (x) represents the net profit (in dollars) and x represents the number of T-shirts sold.1. What is the ordered pair of the y - intercept?2. What does the y - intercept mean in this problem?3. How many t-shirts must be sold in order to make a profit, p(x) >0?

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

p (x) = 15x - 2,500

p (x) = net profit ($)

x = number of t-shirts

Step 02:

1. y - intercept

x = 0

y = 15x - 2500

y = 15(0) - 2500

y = -2500

( 0 , -2500)

Step 03:

The y-intercept means that if you don't sell any T-shirts, there will be a loss of $ 2,500.

Step 04:

p(x) >0

15x - 2500 > 0

15x -2500 + 2500 > 2500

15x > 2500

15x / 15 > 2500 / 15

x > 166.67

More than 167 t-shirts must be sold to make a profit.

That is the full solution.