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 EMV for selling roses is to buy _____ dozen roses.
A)100
B)200
C)400
D)600

Question

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 or reduced profit for selling any unsold roses at $5 a dozen.1. For 100 dozen roses:- If 100 are sold: Profit = $(20 - 10) * 100 = $1000- If 200 are sold: Not applicable, as only 100 are available.- If 400 are sold: Not applicable, as only 100 are available.EMV = $1000 * 0.2 = $2002. For 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: Not applicable, as only 200 are available.EMV = $500 * 0.2 + $2000 * 0.4 = $100 + $800 = $9003. For 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 = -$100 + $0 + $1600 = $1500The highest EMV is for purchasing 400 dozen roses, making it the optimal choice.

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