Math Problem Statement

Determine the profit-maximizing price for Spencer Electronics given the fixed and variable costs and estimated sales quantities at various price points.

Solution

The image contains a problem titled "Determining the Profit-Maximizing Price" related to Spencer Electronics. The goal is to find the price per unit that maximizes company profit, using the given cost data. Let's break down the process to solve this:

Step-by-Step Plan:

A. Calculate Expected Profit for Each Price:

  1. Costs Involved:

    • Fixed Costs: $160,000
    • Variable Costs:
      • Production: $28.00 per unit
      • Shipping: $5.00 per unit
      • Cable company fee: 20% of the selling price
  2. Contribution Margin (CM): The contribution margin per unit is the selling price minus the total variable costs (production, shipping, and cable fee).

    • Total variable cost = Production cost + Shipping cost + Cable company fee (20% of sales price)
  3. Total CM: Multiply the contribution margin per unit by the quantity sold at that price.

  4. Profit Calculation: Profit = Total CM - Fixed Costs

I'll calculate these values for each of the given price points.

B. Determine the Profit-Maximizing Price:

After calculating profits at each price, the price with the highest profit will be the optimal price.

Let me go ahead and calculate these values.Here are the results of the profit calculations for each price point:

Price per UnitQuantityTotal Variable Cost per UnitCM per UnitTotal CMProfit
$8515,000$50.00$35.00$525,000$365,000
$7520,000$48.00$27.00$540,000$380,000
$6525,000$46.00$19.00$475,000$315,000
$5535,000$44.00$11.00$385,000$225,000
$4545,000$42.00$3.00$135,000-$25,000

Analysis for Part B:

  • The $75 price maximizes the company's profit at $380,000.
  • As the price decreases, even though the quantity sold increases, the contribution margin per unit declines significantly, lowering total profit.
  • Lower prices ($55, $45) result in lower profits or even losses.

The price of $75 is optimal because it balances both a reasonable quantity of units sold and a relatively high contribution margin per unit, leading to the highest overall profit.


Do you want more details or have any questions about this calculation?
Here are 5 questions related to this content:

  1. How would increasing fixed costs impact the profit-maximizing price?
  2. What if the cable fee percentage changed from 20% to 25%?
  3. How is contribution margin used in business decision-making?
  4. How can variable costs be reduced to improve profitability?
  5. Would selling at a loss ever be a strategic business decision?

Tip: To improve profitability, companies can explore ways to reduce variable costs, such as negotiating better supplier terms or optimizing production efficiency.

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Math Problem Analysis

Mathematical Concepts

Profit Maximization
Cost Analysis
Contribution Margin
Break-even Analysis

Formulas

Total Variable Cost per Unit = Production Cost + Shipping Cost + (20% of Sales Price)
Contribution Margin per Unit = Sales Price - Total Variable Cost per Unit
Total Contribution Margin = Contribution Margin per Unit × Quantity
Profit = Total Contribution Margin - Fixed Costs

Theorems

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Suitable Grade Level

Undergraduate Business or Economics Level