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 = mg + b.

a) C = 40x + 800
b) C = 40x + 1200
c) C = 50x + 1200
d) C = 50x + 800

Answer 1

The cost equation in the form C = mg + b is C = $60x - $1800.

Step-by-step explanation:

To write the cost equation in the form C = mg + b, we need to determine the values of m and b. The cost C is linearly related to the output x, which represents the number of skateboards produced.

We are given two data points:

When x = 50, C = $1200

When x = 100, C = $4200

To find m, we can calculate the change in C (ΔC) and the change in x (Δx) between the two data points:

ΔC = $4200 - $1200 = $3000

Δx = 100 - 50 = 50

Now we can calculate m:

m = ΔC/Δx = $3000/50 = $60

To find b, we can substitute the values of C and x from one of the data points into the equation:

$1200 = $60(50) + b

b = $1200 - $60(50) = $1200 - $3000 = -$1800

Therefore, the cost equation in the form C = mg + b is:

C = $60x - $1800