Question

2. Angie Pansy manages a downtown flower shop. Flowers must be ordered three days in advance from her supplier in Mexico. Leading up to most holidays (such as Valentine’s Day), sales are almost entirely last-minute. Angie must decide how many dozen roses (25, 50, 100, or 125) to order to meet customer demand. She buys roses for $17 per dozen and sells them for $45 per dozen. Fill in the payoff table (Using Excel - calculate profit for each combination of dozen roses ordered and dozen demanded).

Roses demanded 25 dozen 50 dozen 100 dozen 125 dozen

Roses ordered 25 dozen 50 dozen 100 dozen 125 dozen

Assume the probability of demand is determined as in the table below.

Demand 25 dozen 50 dozen 100 dozen 125 dozen

Probability .10 .25 .45 .20

Using the probabilities given:

a. Calculate the EMV for each alternative order size.

b. How many dozen roses should be ordered if the EMV was used?

c. Calculate the EVwithPI and the EVof PI for this problem.

d. How would you interpret the EVof PI?

Answer 1

a)

Cost per Dozen				17
Selling price per dozen				45
				28
	Probabilities	0.1	0.25	0.45	0.2	Expected Payoff
	Demand	25	50	100	125
Ordered Quantity	25	700	700	700	700	700
	50	275	1400	1400	1400	1287.5
	100	-575	550	2800	2800	1900
	125	-1000	125	2375	3500	1700

b)

EVM for order quantity 100 is maximum. So 100 dozen roses should be ordered

c)

EV with PI :

EV|PI = 0.1*700 + 0.25*1400 + 0.45*2800+0.20*3500 = 2380

That is, given each market direction, we choose the order quantity that maximizes the profit.

EVPI = EV|PI - EVM = 2380-1900 = 480

d)

Knowing the exact demand for roses, he/she should could earn $480 extra. So the information worth is $480