GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsEasy
A production manager is analyzing the cost of manufacturing a new product. The fixed costs for setting up the production line are $5,000, and the variable cost per unit produced is $15. If 'C' represents the total cost and 'x' represents the number of units produced, which equation models the total cost?
- AC = x + 5000 + 15
- BC = 5000 - 15x
- CC = 5000x + 15
- DC = 15x + 5000
Show answer & explanationAnswer & explanation
Correct answer: D. C = 15x + 5000
The total cost is the sum of fixed costs and variable costs. Fixed costs are constant, while variable costs depend on the number of units produced. Therefore, the equation is C = (cost per unit * units) + fixed cost.
Why the other options are wrong
- A. This incorrectly treats both the variable cost and the number of units as separate additions to the fixed cost.
- B. This incorrectly subtracts the variable cost from the fixed cost, and also incorrectly assigns the variable cost and fixed cost roles.
- C. This incorrectly assigns the fixed cost to be dependent on the number of units and the variable cost as a constant.
Linear Cost Function
A linear cost function models the total cost (C) as a sum of fixed costs and variable costs, where variable costs are directly proportional to the number of units produced (x).
- C = mx + b, where m is variable cost per unit and b is fixed cost.
- Fixed costs are incurred regardless of production volume.
- Variable costs change with the production volume.
Memory trick: Fixed costs are your party's base fee, variable costs are per guest.