Math Problem Statement

At a production level of 7,150 units, a project has total cash costs of $142,673. The variable cost per unit is $9.28, and the depreciation is $4,200. What is the amount of the total fixed costs?

Multiple Choice $70,552 $72,121 $66,352 $76,321 $80,521

Solution

To find the total fixed costs, we can use the following formula for total cash costs:

Total Cash Costs=(Variable Cost per Unit×Number of Units)+Fixed Costs\text{Total Cash Costs} = (\text{Variable Cost per Unit} \times \text{Number of Units}) + \text{Fixed Costs}

Where:

  • Total Cash Costs = $142,673
  • Variable Cost per Unit = $9.28
  • Number of Units = 7,150
  • Fixed Costs = ?

Step-by-step calculation:

  1. Calculate total variable costs: Total Variable Costs=9.28×7,150=66,752\text{Total Variable Costs} = 9.28 \times 7,150 = 66,752

  2. Plug values into the total cash costs equation: 142,673=66,752+Fixed Costs142,673 = 66,752 + \text{Fixed Costs}

  3. Solve for fixed costs: Fixed Costs=142,67366,752=75,921\text{Fixed Costs} = 142,673 - 66,752 = 75,921

Since depreciation is part of fixed costs, we add the depreciation to this value:

  1. Add depreciation to fixed costs: Total Fixed Costs=75,921+4,200=80,121\text{Total Fixed Costs} = 75,921 + 4,200 = 80,121

Thus, the total fixed costs (including depreciation) are approximately $80,121, but none of the given choices matches this exactly. The closest option is $80,521.

Answer:

$80,521

Would you like further details on the calculation? Here are some follow-up questions:

  1. How does depreciation impact fixed costs?
  2. What are the differences between fixed and variable costs in project budgeting?
  3. How could a change in production level affect the variable cost calculation?
  4. What other factors could influence total cash costs in a project?
  5. What is the significance of cash flow analysis in production management?

Tip: Always check if depreciation is included or needs to be added when calculating fixed costs.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Cost Accounting

Formulas

Total Cash Costs = (Variable Cost per Unit × Number of Units) + Fixed Costs
Total Fixed Costs = Fixed Costs + Depreciation

Theorems

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Suitable Grade Level

Grades 10-12