Blossom's Flowers purchases roses for sale for Valentine's Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine's Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine's Day: 100, 200, or 400 dozen roses. Given 0.2, 0.4, and 0.4 are the probabilities for the sale of 100, 200, or 400 dozen roses, respectively, what is the optimal EOL for buying roses?

Question

Quizplus · Accepted Answer

To find the optimal EOL (Expected Opportunity Loss), we need to calculate the expected value for each buying option and subtract the maximum value from it.

Let's start with the 100 dozen roses option:
- Probability of this option being chosen = 0.2
- Cost of buying 100 dozen roses = $10 * 100 = $1000
- Revenue if all roses are sold = $20 * 100 = $2000
- Revenue if leftover roses are sold = $5 * 100 = $500
- Expected value = (0.2 * $2000) + (0.8 * $500) - $1000 = $300
- Opportunity loss = $1700 (since $2000 is the maximum value)

Moving on to the 200 dozen roses option:
- Probability of this option being chosen = 0.4
- Cost of buying 200 dozen roses = $10 * 200 = $2000
- Revenue if all roses are sold = $20 * 200 = $4000
- Revenue if leftover roses are sold = $5 * 200 = $1000
- Expected value = (0.4 * $4000) + (0.6 * $1000) - $2000 = $600
- Opportunity loss = $1400 (since $4000 is the maximum value)

Finally, the 400 dozen roses option:
- Probability of this option being chosen = 0.4
- Cost of buying 400 dozen roses = $10 * 400 = $4000
- Revenue if all roses are sold = $20 * 400 = $8000
- Revenue if leftover roses are sold = $5 * 400 = $2000
- Expected value = (0.4 * $8000) + (0.6 * $2000) - $4000 = $2400
- Opportunity loss = $5600 (since $8000 is the maximum value)

So, the optimal EOL is $1400 which occurs when 200 dozen roses are purchased. Therefore, the best choice is option B, $700.

Blossom's Flowers Purchases Roses for Sale for Valentine's Day