Solution for Problem 1.2.3

A company's cost is represented by C = 120x +10,000 where x is the number of units sold. The company sells each unit for $300 so revenue is R = 300x. How much did the company make if they sell 50 units. 100 units?

Quantities

Step
Revenue R = 300x
Cost C = 120x + 10,000

Let x = Number of Units

Let P = Profit
P = R - C = 300x - (120x + 10,000)
300x - 120x - 10,000 = 180x - 10,000

P = 180x - 10,000

Identify the known quantities.

 

Identify the unknown quantities.

Profit = Revenue - Costs

Create a model (or equation)

Use the Formula

For 50 units, let x = 50.
R = 180(50) - 10,000 = 9,000 -10,000 = -1,000  
R =  -$1,000  Lost money

For 100 units, let x = 100.
R = 180(100) - 10,000 = 18,000 -10,000 = 8,000 
R =  $8,000