Problem 669

Kara’s Custom Tees experienced fixed cost of 400 and variable cost of 5 a shirt. Write an equation that can be used to determine the total expenses encountered by Kara’s Custom Tees. Let x be the number  of shirt, and let C(x) be the total cost of producing x shirt. Then, calculate the cost of producing 8 shirts.

 

Solution:-

 

Notice that the cost of producing zero shirt is the fixed 400. Write the point (0,400)as a solution to the equation.

If 10 shirts are produced, the total cost 450.

Write a second point(10,450) as a solution to the equation.

Next , find the slope of the line through the point, (0,400) and (10,450).

m  = \frac{450 - 400}{10} = 5

Since  (0,400) is the y-intercept and 5 is the slope, use the formula y = mx + b

to write the equation. In this case, y = C(x), m = 5, and b = 400.

Thus, C(x) = 5x + 400.

By plotting the two point, you get graph of C(x) = 5x + 400 with domain [0,\infty).

Calculate the cost of  producing 8 shirts. In other world, find C(8).

C(8) = 5(8) + 400

C(8) = 40 +400

C(8) = 440

The cost of producing 8 shirt is 440.

 

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