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
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. The payoff for buying 200 dozen roses and selling 100 dozen roses at the full price is
Well, let's crunch some numbers and find out! In order to calculate the optimal EOL (Expected Outcome Level), we need to consider the potential outcomes and their associated probabilities.
For each of the three amounts of roses, we have the following potential outcomes on Valentine's Day:
- If 100 dozen roses are purchased, the probabilities of selling all, some, or none are 0.2, 0.6, and 0.2, respectively.
- If 200 dozen roses are purchased, the probabilities of selling all, some, or none are 0.4, 0.5, and 0.1, respectively.
- If 400 dozen roses are purchased, the probabilities of selling all, some, or none are 0.4, 0.4, and 0.2, respectively.
Based on these probabilities, we can calculate the expected outcomes (EO) for each scenario.
For 100 dozen roses:
EO = (0.2 * (20 * 100)) + (0.6 * (20 * x)) + (0.2 * (5 * 100))
= 400 + (12 * x) + 100
= 500 + (12 * x)
For 200 dozen roses:
EO = (0.4 * (20 * 200)) + (0.5 * (20 * y)) + (0.1 * (5 * 200))
= 1600 + (10 * y) + 100
= 1700 + (10 * y)
For 400 dozen roses:
EO = (0.4 * (20 * 400)) + (0.4 * (20 * z)) + (0.2 * (5 * 400))
= 3200 + (8 * z) + 400
= 3600 + (8 * z)
To find the optimal EOL, we should choose the option that maximizes the expected outcome. This means we need to maximize the EO function for each scenario.
However, since we don't have any specific values for "x," "y," or "z," we can't determine the optimal EOL with certainty. We would need more information regarding the expected sales of roses for each amount to calculate the optimal EOL accurately.
So, in conclusion, the optimal EOL for buying roses is dependent on the expected sales and cannot be determined without additional information. Hey, at least I didn't thorn my way out of the problem!
To determine the optimal EOL (Expected Optimal Level) for buying roses, we first need to calculate the expected profit for each potential purchase amount of roses.
Let's calculate the expected profit for buying 100 dozen roses:
The cost of purchasing 100 dozen roses = 100 * $10 = $1000
The revenue from selling 100 dozen roses = 100 * $20 = $2000
The profit from selling 100 dozen roses = $2000 - $1000 = $1000
The probability of selling 100 dozen roses = 0.2
Expected profit for buying 100 dozen roses = 0.2 * $1000 = $200
Now, let's calculate the expected profit for buying 200 dozen roses:
The cost of purchasing 200 dozen roses = 200 * $10 = $2000
The revenue from selling 200 dozen roses = 200 * $20 = $4000
The profit from selling 200 dozen roses = $4000 - $2000 = $2000
The probability of selling 200 dozen roses = 0.4
Expected profit for buying 200 dozen roses = 0.4 * $2000 = $800
Lastly, let's calculate the expected profit for buying 400 dozen roses:
The cost of purchasing 400 dozen roses = 400 * $10 = $4000
The revenue from selling 400 dozen roses = 400 * $20 = $8000
The profit from selling 400 dozen roses = $8000 - $4000 = $4000
The probability of selling 400 dozen roses = 0.4
Expected profit for buying 400 dozen roses = 0.4 * $4000 = $1600
To find the optimal EOL, we select the purchase amount that maximizes the expected profit. Therefore, the optimal EOL for buying roses is the purchase amount with the highest expected profit, which is 400 dozen roses with an expected profit of $1600.
To determine the optimal expected monetary value (EOL) for purchasing roses, we need to calculate the expected profit for each possible purchase quantity (100, 200, and 400 dozen roses).
Let's start by calculating the profit for each purchase quantity:
For 100 dozen roses:
- Cost of purchasing: $10 x 100 = $1000
- Revenue from sales: $20 x 100 = $2000
- Unsold roses: 100 - 0.2(100) = 100 - 20 = 80 dozen
- Revenue from unsold roses: $5 x 80 = $400
- Profit: $2000 - $1000 + $400 = $1400
For 200 dozen roses:
- Cost of purchasing: $10 x 200 = $2000
- Revenue from sales: $20 x 200 = $4000
- Unsold roses: 200 - 0.4(200) = 200 - 80 = 120 dozen
- Revenue from unsold roses: $5 x 120 = $600
- Profit: $4000 - $2000 + $600 = $2400
For 400 dozen roses:
- Cost of purchasing: $10 x 400 = $4000
- Revenue from sales: $20 x 400 = $8000
- Unsold roses: 400 - 0.4(400) = 400 - 160 = 240 dozen
- Revenue from unsold roses: $5 x 240 = $1200
- Profit: $8000 - $4000 + $1200 = $5200
Now, let's calculate the expected profit by considering the probabilities:
Expected profit = (Profit for 100 dozen roses x Probability) + (Profit for 200 dozen roses x Probability) + (Profit for 400 dozen roses x Probability)
Expected profit = ($1400 x 0.2) + ($2400 x 0.4) + ($5200 x 0.4)
Expected profit = $280 + $960 + $2080
Expected profit = $4320
Therefore, the optimal EOL for buying roses would be to purchase 400 dozen roses. This would yield an expected profit of $4320.