Problem 18 The local Office of Tourism sells souvenir calendars. Sue, the head o
ID: 428700 • Letter: P
Question
Problem 18 The local Office of Tourism sells souvenir calendars. Sue, the head of the office, needs to order these calendars in advance of the main tourist season. Based on past seasons, Sue has determined the probability of selling different quantities of the calendars for a particular tourist season. Probability of Demand 0.15 0.25 0.30 0.20 0.10 Demand for Calendars 75,000 80,000 85,000 90,000 95,000 The Office of Tourism sells the calendars for $12.95 each. The calendars cost Sue $5 each. The salvage value is estimated to be $0.50 per unsold calendar. Determine how many calendars Sue should order to maximize expected profitsExplanation / Answer
Selling price (S) = $12.95
Cost price (C) = $5
Salvage value (g) = $0.50
Penalty cost (B) = 0
For optimal quantity for maximum expected profits, the following condition is the optimality condition.
P (Q- 1) < Cu / ( Co + Cu ) < P (Q)
where Cu is the cost of underage, Co is the cost of overage and Q is the optimal quantity
Cu = S - C + B
Co = C - g
Cu / ( Co + Cu ) = (S - C + B) / (S - g + B)
From the current values for this particular question, the above value is equal to
= (12.95 - 5 + 0) / (12.95 - 0.50 + 0)
= 0.638
From the table, we can see that P(80000) < 0.638 < P(85000)
Hence from our above definition, the number of calenders that Sue should order to maximize expected profits is 85000.
Demand (Q) 75000 80000 85000 90000 95000 Probability of demand 0.15 0.25 0.30 0.20 0.10 Cumulative demand P(Q) 0.15 0.40 0.70 0.90 1