Question

A company that manufactures skateboards can produce 50 skateboards a day at a cost of $1200 and can produce 100 skateboards a day at a cost of $4200. Assume that cost (C) is linearly related to the output (x). Write the Cost Equation in the form (C = mx + b).

a. (C = 38x + 1200)
b. (C = 32x + 1200)
c. (C = 38x + 4200)
d. (C = 32x + 4200)

Answer 1

The cost equation in the form C = mx + b for a company that manufactures skateboards is C = 60x - 1800.

Step-by-step explanation:

To write the cost equation in the form C = mx + b, where C represents the cost and x represents the output, we can use the given information about the cost and output of the company that manufactures skateboards.

Let's use the two points (50, 1200) and (100, 4200) to find the slope (m) and the y-intercept (b) of the equation.

Slope (m) = (y2 - y1)/(x2 - x1) = (4200 - 1200)/(100 - 50) = 3000/50 = 60

y-intercept (b) = y - mx = 1200 - 60 * 50 = 1200 - 3000 = -1800

Therefore, the cost equation in the form C = mx + b is (C = 60x - 1800).