Math Problem Statement

The market price is $10 per product and the average variable cost is six dollars per product. The average fix cost is three dollars per product and they sell 300 units then what kind of profit would the company

Solution

To determine the company's profit, we need to calculate both total revenue and total cost, and then find the difference between them.

Step 1: Calculate Total Revenue (TR)

Total revenue is calculated by multiplying the market price per product by the number of units sold:

TR=Price per unit×Number of units soldTR = \text{Price per unit} \times \text{Number of units sold} TR=10×300=3000dollarsTR = 10 \times 300 = 3000 \, \text{dollars}

Step 2: Calculate Total Cost (TC)

Total cost consists of total variable cost (TVC) and total fixed cost (TFC). Let's calculate both:

  1. Total Variable Cost (TVC): TVC=Average variable cost×Number of units soldTVC = \text{Average variable cost} \times \text{Number of units sold} TVC=6×300=1800dollarsTVC = 6 \times 300 = 1800 \, \text{dollars}

  2. Total Fixed Cost (TFC): TFC=Average fixed cost×Number of units soldTFC = \text{Average fixed cost} \times \text{Number of units sold} TFC=3×300=900dollarsTFC = 3 \times 300 = 900 \, \text{dollars}

Now, sum these to get the total cost: TC=TVC+TFC=1800+900=2700dollarsTC = TVC + TFC = 1800 + 900 = 2700 \, \text{dollars}

Step 3: Calculate Profit

Profit (π) is the difference between total revenue and total cost:

π=TRTC\pi = TR - TC π=30002700=300dollars\pi = 3000 - 2700 = 300 \, \text{dollars}

Conclusion:

The company's profit is $300.

Would you like more details on any of the steps?

Here are 5 related questions:

  1. What happens to profit if the market price increases?
  2. How does a change in variable costs impact profit?
  3. What if the company sold more or fewer units?
  4. How does average fixed cost change with the number of units sold?
  5. How can the company improve profitability?

Tip: Profit increases if you reduce variable costs while maintaining or increasing the price of the product.

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Math Problem Analysis

Mathematical Concepts

Revenue Calculation
Cost Analysis
Profit Calculation

Formulas

Total Revenue (TR) = Price per unit × Number of units sold
Total Variable Cost (TVC) = Average variable cost × Number of units sold
Total Fixed Cost (TFC) = Average fixed cost × Number of units sold
Total Cost (TC) = TVC + TFC
Profit (π) = TR - TC

Theorems

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Suitable Grade Level

Grades 9-12