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, then the optimal EMV for buying roses is

1500

To find the Expected Monetary Value (EMV) for buying roses, we need to calculate the expected value for each possible outcome and then determine the optimal option with the highest EMV.

Let's calculate the EMV for each possible purchase amount:

For the purchase of 100 dozen roses:
- Probability: 0.2
- Cost: $10 x 100 = $1000
- Revenue if sold on Valentine's Day: $20 x 100 = $2000
- Revenue if unsold on Valentine's Day: $5 x 100 = $500
- EMV = (Revenue on Valentine's Day x Probability) + (Revenue if unsold x Probability) - Cost
= ($2000 x 0.2) + ($500 x 0.2) - $1000
= $400 + $100 - $1000
= -$500

For the purchase of 200 dozen roses:
- Probability: 0.4
- Cost: $10 x 200 = $2000
- Revenue if sold on Valentine's Day: $20 x 200 = $4000
- Revenue if unsold on Valentine's Day: $5 x 200 = $1000
- EMV = (Revenue on Valentine's Day x Probability) + (Revenue if unsold x Probability) - Cost
= ($4000 x 0.4) + ($1000 x 0.4) - $2000
= $1600 + $400 - $2000
= $0

For the purchase of 400 dozen roses:
- Probability: 0.4
- Cost: $10 x 400 = $4000
- Revenue if sold on Valentine's Day: $20 x 400 = $8000
- Revenue if unsold on Valentine's Day: $5 x 400 = $2000
- EMV = (Revenue on Valentine's Day x Probability) + (Revenue if unsold x Probability) - Cost
= ($8000 x 0.4) + ($2000 x 0.4) - $4000
= $3200 + $800 - $4000
= $0

After calculating the EMV for each purchase amount, we find that the optimal EMV is $0, which means there is no profit or loss expected. Both the purchase of 200 dozen roses and the purchase of 400 dozen roses have the same EMV of $0. Therefore, either option would be equally optimal in terms of maximizing expected value.