TABLE 19-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature
-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 0.6 are the probabilities for the sale of 100,200,or 400 dozen roses,respectively,then the optimal EMV for buying roses is
A)$700.
B)$900.
C)$1,700.
D)$1,900.

Question

TABLE 19-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature  
-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 0.6 are the probabilities for the sale of 100,200,or 400 dozen roses,respectively,then the optimal EMV for buying roses is
A)$700. 
B)$900. 
C)$1,700. 
D)$1,900.

Quizplus · Accepted Answer

First, we need to calculate the expected income for each alternative:

- Alternative 1: Buy 100 dozen roses
    - Probability of selling 100 dozen roses = 0.2
    - Income from selling 100 dozen roses = $20 x 100 = $2,000
    - Income from selling leftover roses = $5 x 100 = $500
    - Expected income = (0.2 x $2,000) + (0.8 x $500) = $700
    
- Alternative 2: Buy 200 dozen roses
    - Probability of selling 200 dozen roses = 0.4
    - Income from selling 200 dozen roses = $20 x 200 = $4,000
    - Income from selling leftover roses = $5 x 200 = $1,000
    - Expected income = (0.4 x $4,000) + (0.6 x $1,000) = $2,200
    
- Alternative 3: Buy 400 dozen roses
    - Probability of selling 400 dozen roses = 0.6
    - Income from selling 400 dozen roses = $20 x 400 = $8,000
    - Income from selling leftover roses = $5 x 400 = $2,000
    - Expected income = (0.6 x $8,000) + (0.4 x $2,000) = $5,600
    
Based on the expected incomes, the optimal EMV is to buy 400 dozen roses (Alternative 3) with an expected income of $5,600. Therefore, the answer is D.

TABLE 19-1 The Following Payoff Table Shows Profits Associated with a Set