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 EMV for buying roses?

Question

Quizplus · Accepted Answer

Expected Monetary Value (EMV) for buying 100 dozen roses:
Revenue from selling 100 dozen roses = (0.2 x 20 x 100) = $400
Cost of buying 100 dozen roses = 10 x 100 = $100
Expected Monetary Value = Revenue - Cost= $400 - $100 = $300

EMV for buying 200 dozen roses:
Revenue from selling 200 dozen roses = (0.4 x 20 x 200) = $1,600
Cost of buying 200 dozen roses = 10 x 200 = $2,000
Expected Monetary Value = Revenue - Cost = $1,600 - $2,000 = -$400 (loss)

EMV for buying 400 dozen roses:
Revenue from selling 400 dozen roses = (0.4 x 20 x 400) = $3,200
Cost of buying 400 dozen roses = 10 x 400 = $4,000
Expected Monetary Value = Revenue - Cost = $3,200 - $4,000 = -$800 (loss)

Therefore, the optimal EMV is obtained by purchasing 100 dozen roses with an EMV of $300.

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