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
1000
To determine the optimal EOL (Expected Optimal Level) for buying roses, we need to calculate the expected profit for each possible quantity of roses.
Let's calculate the expected profit for purchasing 100 dozen roses:
- The probability of selling 100 dozen roses is 0.2.
- The profit per dozen roses sold is $20 - $10 = $10.
- So, the expected profit for selling 100 dozen roses is 100 * $10 * 0.2 = $200.
Next, let's calculate the expected profit for purchasing 200 dozen roses:
- The probability of selling 200 dozen roses is 0.4.
- The profit per dozen roses sold is $20 - $10 = $10.
- So, the expected profit for selling 200 dozen roses is 200 * $10 * 0.4 = $800.
Finally, let's calculate the expected profit for purchasing 400 dozen roses:
- The probability of selling 400 dozen roses is 0.4.
- The profit per dozen roses sold is $20 - $10 = $10.
- So, the expected profit for selling 400 dozen roses is 400 * $10 * 0.4 = $1600.
Now, we can compare the expected profits for each quantity of roses:
- 100 dozen roses: $200
- 200 dozen roses: $800
- 400 dozen roses: $1600
Based on these calculations, the optimal EOL for buying roses would be to purchase 400 dozen roses, as it has the highest expected profit.