Question

A company that manufactures widgets has fixed costs of $8,906.00 each month and a cost of $2.64 for each widget it produces. Which of the following equations could be used to determine the total production costs for the company if it produced x widgets last month?

(Let x represent the number of widgets the factory produced last month and y represent the total production costs for the factory.)
A.
y = $890.60 + $2.64x
B.
y = $8,906.00 + $2.64x
C.
y = $8,906.00x - $2.64x
D.
y = $2.64 + $8,906.00x

Answer 1

The equation could be used to determine the total production costs for the company if it produced x widgets last month is

y = $8,906.00 + $2.64x ⇒ B

Explanation:

The form of the linear equation is y = m x + b, where

• m is the slope ⇒ rate of change

• b is the y-intercept ⇒ initial amount

∵ A company has fixed costs of $8,906.00 each month

→ That means it is a fixed value every month

∴ b = 8,906.00

∵ The cost of each widget it produces is $2.64 for

→ That means the value is changing according to the number of widgets

∴ m = 2.64

∵ y represents the total costs of production last month

∵ x represents the number of widgets the factory produced last month

→ Substitute the values of m and b in the form of the equation above

∴ y = 2.64x + 8,906.00

The equation could be used to determine the total production costs for the company if it produced x widgets last month is

y = $8,906.00 + $2.64x