To determine which pizza Sammie's Pizza should promote to maximize profits, we need to calculate the contribution margin for each pizza type and compare their contribution margin per unit and total contribution margin.

Step 1: Definitions

• Contribution Margin (CM): The contribution margin is the difference between the selling price and the variable cost per unit. It's the amount left to cover fixed costs and contribute to profit.

  $CM = \text{Selling Price} - \text{Variable Cost}$

• Contribution Margin Ratio (CMR): The contribution margin ratio expresses the contribution margin as a percentage of the selling price.

  $CMR = \frac{CM}{\text{Selling Price}} \times 100$

Step 2: Calculate Contribution Margin for Single-Topping Pizzas

• Selling Price for Single-Topping Pizza: $8
• Variable Cost for Single-Topping Pizza: $2

$CM_{\text{single}} = 8 - 2 = 6 \, \text{dollars}$

Now, calculate the CM ratio for single-topping pizzas:

$CMR_{\text{single}} = \frac{6}{8} \times 100 = 75\%$

Step 3: Calculate Contribution Margin for Supreme Pizzas

• Selling Price for Supreme Pizza: $12
• Variable Cost for Supreme Pizza: $6

$CM_{\text{supreme}} = 12 - 6 = 6 \, \text{dollars}$

Now, calculate the CM ratio for supreme pizzas:

$CMR_{\text{supreme}} = \frac{6}{12} \times 100 = 50\%$

Step 4: Calculate Total Contribution Margin

To calculate the total contribution margin for each type of pizza, we need to consider the sales distribution.

• 20% of 150 pizzas are single-topping pizzas.

  $\text{Singles sold per week} = 0.20 \times 150 = 30$

  Total contribution margin for single-topping pizzas:

  $\text{Total CM}_{\text{single}} = 30 \times 6 = 180 \, \text{dollars}$

• 80% of 150 pizzas are supreme pizzas.

  $\text{Supremes sold per week} = 0.80 \times 150 = 120$

  Total contribution margin for supreme pizzas:

  $\text{Total CM}_{\text{supreme}} = 120 \times 6 = 720 \, \text{dollars}$

Step 5: Conclusion

• Contribution Margin per Unit: Both single-topping and supreme pizzas have the same contribution margin per unit of $6.
• Contribution Margin Ratio: Single-topping pizzas have a higher contribution margin ratio (75%) than supreme pizzas (50%).
• Total Contribution Margin: Supreme pizzas contribute significantly more to the total contribution margin ($720) than single-topping pizzas ($180).

Thus, the best strategy for maximizing profit is to promote supreme pizzas, because they generate the highest total contribution margin.

Correct Answer:

B. Supremes because they have the highest contribution margin ratio.

Would you like to explore more details or have any questions about this problem?

Here are some follow-up questions to deepen your understanding:

1. How do fixed costs affect the overall profitability of each pizza type?
2. What impact would a change in variable costs have on the contribution margin?
3. If sales of supreme pizzas increased by 10%, how would that impact the total contribution margin?
4. How would you calculate the breakeven point for each pizza type?
5. What if the price of supreme pizzas was reduced by $1? Would it still be the best pizza to promote?

Tip: Always compare both the unit contribution margin and the total contribution margin when making decisions about product promotion.