Question

Tanya must decide how many cream puffs to prepare this coming Saturday night for her cafe's diners. She has the option to make 50, 100, or 150 cream puffs. Assume that the demand for the cream puffs is 50, 100, or 150. Each pastry costs $5 to make and sells for $7. Unsold puffs are donated to the food bank and there is no opportunity cost for lost sales. Tanya got the following probability information for the pies: P(50) = 0.3, P(100) = 0.5, P(150) = 0.2.

Tanya discovered the Hurwicz approach and decided to apply this using α= 0.8. Her decision should be to prepare how many cream puffs?

Answer 1

Cost	5
Sells for	7
Profit	2
Unsold	0

The table for different make and demand combinations is as given:

Make/Demand	50	100	150
50	100	100	100
100	-150	200	200
150	-400	-50	300

For example if Tanya makes 50 and demand is 100, her total profit = 50X(7-5) = 100

If Tanya makes 100 and demand is 50, total profit = 50X(7-5) - 50(5) = 100 - 250 = -150 and so on

Now for Hurwicz criterion, we calculate maximum Hmax and minimum Hmin for each make option

Then using alpha = 0.8, for each option we calculate H = HmaxXalpha + HminX(1-alpha)

Make/Demand	50	100	150	Hmax	Hmin	H
50	100	100	100	100	100	100
100	-150	200	200	200	-150	130
150	-400	-50	300	300	-400	160

hence we get maximum value of H 160 for the qty 150

i.e. Tanya should make 150 cream puffs