Question

Rally​ Co.'s fixed costs to produce toy trucks are​ $200,000. The variable costs to produce each truck are​ $4. They will price the trucks at​ $20.

What is their total sales​ (revenue) when they​ break-even?

Answer 1

Their total sales (revenue) when they break-even is $250,000

Explanation:

Linear Modeling

Some situations can be mathematically represented as linear functions. If we are in a situation where a linear model is suitable, then we need two independent data to build it up.

The linear function can be expressed in the slope-intercept format:

y = mx + b

Where m and b are constant values.

The total cost function for Rally Co.'s to produce x toy trucks is:

C(x) = 200,000 + 4x

Given they sell each truck for $20, the revenue function is:

R(x)= 20x

The break-even condition is when the costs and the revenue are equal:

20x = 200,000 + 4x

Subtracting 4x:

16x = 200,000

Dividing by 16:

x = 200,000/16

x = 12,500 toy trucks

The revenue at this production level is:

R(x)= 20*12,500=250,000

Their total sales (revenue) when they break-even is $250,000