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 EVPI for buying roses is
A)$700
B)$1,500
C)$1,900
D)$2,600

Question

Quizplus · Accepted Answer

To find the expected value of perfect information (EVPI), we need to find the difference between the expected value of the decision with perfect information and the expected value of the decision without perfect information. In this case, if we had perfect information about how many dozens of roses will be sold, we would choose the option (100, 200, or 400) that would maximize our profit.

With perfect information, the probabilities are 0.2 for 100 dozen, 0.4 for 200 dozen, and 0.4 for 400 dozen.

Expected value with perfect information: 
EV = 0.2($10 * 100) + 0.4($10 * 200) + 0.4($10 * 400) = $3,000

Now, we need to find the expected value without perfect information.

Expected value without perfect information:

EV(NPI) = 0.2[$20(100) - $10(100)] + 0.4[$20(200) - $10(200)] + 0.4[$20(400) - $10(400)] + 0.2[$5(400 - N)]

where N is the number of dozens of roses not sold.

We need to maximize this equation by choosing the appropriate value for N.

d(EV(NPI))/dN = 0.2(-5) + 0.4(-10) + 0.4(-20) - 0.2(5) = -10

Since the derivative is negative, it means that EV(NPI) is decreasing as N increases. Therefore, we choose N to be zero (i.e., assuming we sell all the roses on Valentine's Day).

EV(NPI) = 0.2[$20(100) - $10(100)] + 0.4[$20(200) - $10(200)] + 0.4[$20(400) - $10(400)] = $1,800

EVPI = EV - EV(NPI) = $3,000 - $1,800 = $1,200

Therefore, the best choice is to buy 200 dozen roses, since the expected value of this decision ($1,600) is the highest among the three options. However, none of the choices are the best choice(s) when considering the expected value of perfect information.

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