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
1700
To calculate the optimal EMV (Expected Monetary Value) for buying roses, we need to consider the probabilities and potential outcomes.
First, let's calculate the expected profit for each quantity of roses:
1. For 100 dozen roses:
- Probability: 0.2 (20% chance)
- Purchase cost: $10/dozen
- Selling price on Valentine's Day: $20/dozen
- Unsold price after Valentine's Day: $5/dozen
- Potential profit: (20 x $20) + ((1 - 20) x $5)
= $400 + (80 x $5)
= $400 + $400
= $800
2. For 200 dozen roses:
- Probability: 0.4 (40% chance)
- Purchase cost: $10/dozen
- Selling price on Valentine's Day: $20/dozen
- Unsold price after Valentine's Day: $5/dozen
- Potential profit: (40 x $20) + ((1 - 40) x $5)
= $800 + (60 x $5)
= $800 + $300
= $1100
3. For 400 dozen roses:
- Probability: 0.4 (40% chance)
- Purchase cost: $10/dozen
- Selling price on Valentine's Day: $20/dozen
- Unsold price after Valentine's Day: $5/dozen
- Potential profit: (80 x $20) + ((1 - 80) x $5)
= $1600 + (20 x $5)
= $1600 + $100
= $1700
The expected profit for each quantity is:
- For 100 dozen roses: $800
- For 200 dozen roses: $1100
- For 400 dozen roses: $1700
To calculate the EMV, we multiply the profit for each quantity by its corresponding probability and sum them up:
EMV = (0.2 x $800) + (0.4 x $1100) + (0.4 x $1700)
EMV = $160 + $440 + $680
EMV = $1280
Therefore, the optimal EMV for buying roses is $1280.