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 expected monetary value (EMV)for buying 200 dozen roses is _______.

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 expected monetary value (EMV)for buying 200 dozen roses is  _______.

Quizplus · Accepted Answer

For 200 dozen roses:

Probability of selling all: 0.4 x 0.4 = 0.16 
Expected revenue from selling all: $20 x 200 x 0.16 = $640

Probability of selling some: 0.4 x 0.6 + 0.2 x 0.4 = 0.4 
Expected revenue from selling some: $20 x 200 x 0.4 + $5 x (200 - sold) x 0.4 
= $1600 + $140(sold-200)

Probability of selling none: 0.2 x 0.6 = 0.12 
Expected revenue from selling none: $5 x 200 x 0.12 = $120

EMV = Expected revenue from selling all + Expected revenue from selling some + Expected revenue from selling none 
= $640 + $1600 + $140(sold-200) + $120 
= $1,700

Therefore, buying 200 dozen roses has an expected monetary value of $1,700, which is the highest among the three options. The best choice for Blossom's Flowers is to buy 200 dozen roses.

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