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The postal service of St. Vincent, an island in the West Indies, recently introduced a limited edition deluxe souvenir sheet priced at $15.00 each. The initial market response was quite positive, with an increase in unit sales compared to the regular souvenir sheets. The postal service sold a total of 50,000 units of the deluxe souvenir sheet.

Based on the given information, calculate the following:
What was the postal service's increase (decrease) in total contribution margin when it sold 50,000 deluxe souvenir sheets at $15.00 each, compared to selling 80,000 regular souvenir sheets at $8.00 each?
By what percentage did the St. Vincent post office increase the selling price for the deluxe souvenir sheet compared to the regular souvenir sheets? Additionally, calculate the percentage increase in unit sales for the deluxe souvenir sheet compared to the regular souvenir sheets. (Round your answers to one-tenth of a percent.)
If the postal service wants to maintain the same total contribution margin per unit for the deluxe souvenir sheets as it did for the regular souvenir sheets, what selling price should they set for the deluxe souvenir sheet? (Round your answer to the nearest whole dollar.)
Calculate the number of deluxe souvenir sheets the postal service would need to sell at the price determined in question 3 to equal the total contribution margin earned by selling 80,000 regular souvenir sheets at $8.00 each. (Round your answer to the nearest whole number.)
Please show your calculations and provide explanations for each answer.

User Pumbo
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1 Answer

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To calculate the increase (decrease) in total contribution margin, we need to compare the revenue generated by selling the deluxe souvenir sheets to the revenue generated by selling the regular souvenir sheets.

1. Revenue from selling 50,000 deluxe souvenir sheets:

Total revenue = Selling price per unit × Number of units sold

Revenue = $15.00 × 50,000 = $750,000

2. Revenue from selling 80,000 regular souvenir sheets:

Total revenue = Selling price per unit × Number of units sold

Revenue = $8.00 × 80,000 = $640,000

Contribution margin is the difference between revenue and variable costs. Since the variable costs are not given, we'll assume they remain constant for both types of souvenir sheets.

3. Increase (decrease) in total contribution margin:

Increase (decrease) in total contribution margin = Revenue from deluxe sheets - Revenue from regular sheets

= $750,000 - $640,000 = $110,000

The postal service experienced an increase in total contribution margin of $110,000.

To calculate the percentage increase in the selling price for the deluxe souvenir sheet compared to the regular souvenir sheets:

4. Percentage increase in selling price:

Percentage increase = [(Selling price for deluxe - Selling price for regular) / Selling price for regular] × 100%

= [(15 - 8) / 8] × 100% = 87.5%

The selling price for the deluxe souvenir sheet increased by 87.5% compared to the regular souvenir sheets.

To calculate the percentage increase in unit sales for the deluxe souvenir sheet compared to the regular souvenir sheets:

5. Percentage increase in unit sales:

Percentage increase = [(Number of units sold for deluxe - Number of units sold for regular) / Number of units sold for regular] × 100%

= [(50,000 - 80,000) / 80,000] × 100% = -37.5%

The unit sales for the deluxe souvenir sheet decreased by 37.5% compared to the regular souvenir sheets.

If the postal service wants to maintain the same total contribution margin per unit for the deluxe souvenir sheets as it did for the regular souvenir sheets, we need to find the selling price per unit.

6. Selling price per unit to maintain the same total contribution margin:

Selling price per unit = (Revenue from regular sheets + Increase in total contribution margin) / Number of units sold for deluxe

= ($640,000 + $110,000) / 50,000

= $750,000 / 50,000

= $15.00

The postal service should set the selling price for the deluxe souvenir sheet at $15.00 to maintain the same total contribution margin per unit.

To calculate the number of deluxe souvenir sheets needed to equal the total contribution margin earned by selling 80,000 regular souvenir sheets at $8.00 each:

7. Number of deluxe souvenir sheets needed:

Total contribution margin from regular sheets = Selling price per regular sheet - Variable cost per regular sheet

Total contribution margin from regular sheets = $8.00 - Variable cost per regular sheet

Total contribution margin from deluxe sheets = Selling price per deluxe sheet - Variable cost per deluxe sheet

To maintain the same total contribution margin, we set them equal to each other:

$8.00 - Variable cost per regular sheet = $15.00 - Variable cost per deluxe sheet

Variable cost per regular sheet - Variable cost per deluxe sheet = $15.00 - $8.00

Variable cost per regular sheet - Variable cost per deluxe sheet = $7.00

To find the number of deluxe sheets needed to equal the total contribution margin:

Number of deluxe sheets = (Total contribution margin from regular sheets)

User Syed Usama Ahmad
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