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 alternative using expected monetary value (EMV)for selling roses is to buy _______ dozen roses.

Question

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 alternative using expected monetary value (EMV)for selling roses is to buy  _______ dozen roses.

Quizplus · Accepted Answer

To calculate the Expected Monetary Value (EMV) for each option, we first determine the profit for selling at $20 a dozen and the loss for selling any unsold roses at $5 a dozen. For 100 dozen roses:- If 100 are sold: Profit = $(20 - 10) * 100 = $1000- If 200 are sold: Profit = $(20 - 10) * 100 = $1000 (since only 100 are available)- If 400 are sold: Profit = $(20 - 10) * 100 = $1000 (since only 100 are available)EMV = $1000 * 0.2 + $1000 * 0.4 + $1000 * 0.4 = $1000For 200 dozen roses:- If 100 are sold: Profit = $(20 - 10) * 100 + $(5 - 10) * 100 = $500- If 200 are sold: Profit = $(20 - 10) * 200 = $2000- If 400 are sold: Profit = $(20 - 10) * 200 = $2000 (since only 200 are available)EMV = $500 * 0.2 + $2000 * 0.4 + $2000 * 0.4 = $1500For 400 dozen roses:- If 100 are sold: Profit = $(20 - 10) * 100 + $(5 - 10) * 300 = -$500- If 200 are sold: Profit = $(20 - 10) * 200 + $(5 - 10) * 200 = $0- If 400 are sold: Profit = $(20 - 10) * 400 = $4000EMV = -$500 * 0.2 + $0 * 0.4 + $4000 * 0.4 = $1400Thus, buying 200 dozen roses has the highest EMV of $1500, making it the optimal choice.

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