Question

A restaurant plans to order dessert for the next Sunday. Each dessert costs $12 to buy and can be sold for $16. Any unsold dessert can be sold to a coffee shop for $5. The following table, using data for the last few Sundays gives potential demand and properties for them. Demand (D) 80 90 100 110 Probability f(D) 0.20 0.15 0.30 0.25 120 0.10 Compute the value of the maximum average profit. Lütfen birini seçin: O a. 339.5 O b. 337.5 O C.338.5 O d. 336.5 O e. 335.5

Answer 1

Demand	80	90	100	110	120
Probability	0.2	0.15	0.3	0.25	0.1
Cost	12
Selling price	16
Unsold price	5
Average demand = 80X0.2 + 90X0.15 + 100X0.3 + 110X0.25 + 120X0.1 = 99
Profit per unit	4

Demand	Order qty	Qty at full price	Qty unsold	Full profit	Unsold profit	Total profit
80	99	80	19	320	-133	187
90	99	90	9	360	-63	297
100	99	99	0	396	0	396
110	99	99	0	396	0	396
120	99	99	0	396	0	396

We have considered demand as given above with order qty in each scenario as the average expected demand of 99 calculated above

Qty at full price will be minimum of demand and order qty

Qty unsold will be (order qty - demand) if orfer qty is greater than demand

We have then calculated the full price profit as units X profit/unit

For unsold, profit = unitsX profit/unit (here we have a loss per unit of 5-12 = -7 per unit)

Total profit is then calculated by adding above two columns

Now maxiumum average profit is 187X0.2 + 297X0.15 + 396X0.3 + 396X0.25 + 396X0.1 = 339.5

Option a is the correct answer