# Problem 939

Kara’s Custom Tees experienced fixed costs of 450 and variable costs of 5 per shirt. Write an equation that can be used to determine the total expenses, find the cost, C, of producing 20 short, and graph the equation.

Solution:-

Let x be the number of shirt, and C be the  total cost of producing x shirts.

Notice that the cost of producing zero shirts is simply the fixed cost, 450. Write the point (0,450) as a solution to the equation.

If 10 shirt are produced, the total cost is 450 + 5* 10 = 500.

Write a second point (10,500)as a solution to the equation.

Next, find the slope of the line through the two points (0,450) and (10,500).

m =

Since (0, 450) is the y-intercept and 5 is the slope, use the formula

y = mx + b to write the equation. In this case, y = C, m = 5, and b = 450.

Thus , C = 5x + 450.

Calculate the cost of producing 20 shirts.

Substitute 20 for x.

C = 5(20) + 450

= 100 + 450

It would cost 550 to produce 20 shirts.

Plot the point  (0,450) and (20,550), and draw a straight line through them to draw the graph of C = 5x + 450.