Question

DEMAND	Probability	Cumulative Probability
2100	0.05
2300	0.05
2500	0.20
2700	0.29
2900	0.14
3100	0.05
3300	0.22

Each dozen sells for $0.70and costs 0.51 .cookies that are not sold at the end of the day are reduced to 0.27 and sold the following day as day-old merchandise.

a)What is the optimal number of cookies to make?

b)What is the corresponding expected profit?

please tell me the formula to calculate the expected profit?? I want to know which formula is used to fill in the table to calculate the expected profit without using excel?? Thank you

Answer 1

Payoff table to calculate optimal quantity and expected profit

Possible Demand	Probability	Possible supply
		2100	2300	2500	2700	2900	3100	3300
2100	0.05	399	351	303	255	207	159	111
2300	0.05	399	437	389	341	293	245	197
2500	0.2	399	437	475	427	379	331	283
2700	0.29	399	437	475	513	465	417	369
2900	0.14	399	437	475	513	551	503	455
3100	0.05	399	437	475	513	551	589	541
3300	0.22	399	437	475	513	551	589	627
Total expected profit		399	432.7	462.1	474.3	461.56	436.78	407.7

Total expected profit = Probability*profit

a)What is the optimal number of cookies to make?

Optimal number of cookies 2700 as expected profit is highest

b)What is the corresponding expected profit?

Corresponding expected profit = $474.3