I am posting the answer to this because chegg does not already have it. The loca
ID: 326051 • Letter: I
Question
I am posting the answer to this because chegg does not already have it.
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.
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 profits.
ANSWER:
Quantity Probability 75k 0.15 80k 0.25 85k 0.3 90k 0.2 95k 0.1 Demangd Expected Profit 75000 80000 90000 95000 75000 $596,250.00 $596,250.00 $596,250.00 596,250.00 $596,250.00 S 596,250.00 80000 $573,750.00 636,000.00 $636,000.00 $636,000.00 $636,000.00 $ 85000 $576,250.00 613,500.00 $675,750.00 $675,750.00 $675, 750.00 $ 90000 $578,750.00 $591,000.00 $653,250.00 $715,500.00 $715,500.00 S 95000 $581,250.00 $568500.00 S630,750.00 $693,000.00 $755,250.00 S 626,662.50 645,262.50 645,187.50 632,662.50 Order Amt.Explanation / Answer
Given are the following data :
Selling price of calendar = P = $12.95 per calendar
Cost of calendar = C = $ 5 per calendar
Salvage value of calendar = S = $0.5 per calendar
Underage cost = Cu = $12.95 - $ 5 = $7.95
Overage cost = Co = $ 5 - $0.5 = $4.5
Critical ratio = Cu / ( Cu + Co ) =7.95 / ( 7.95 + 4.5 ) = 7.95/12.45 = 0.638
Critical ratio is the probability of the optimum quantity that should be sold to maximize profit
Following table highlights probability of selling following minimum quantities
Following minimum quantity will be sold
Probability that following minimum quantity will be sold
Critical ratio of 0.638 is nearest to probability 0.60 which is the probability that minimum 85K will be sold
Therefore , quantity to be sold to maximize profit = 85K
HIGHEST EXPECTED PROFIT = 85K
Following minimum quantity will be sold
Probability that following minimum quantity will be sold
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