One of your classmates is inviting you into a partnership to sell holiday gift b

ID: 377576 • Letter: O

Question

One of your classmates is inviting you into a partnership to sell holiday gift baskets. He has found a local source of unique baskets made in Thailand. The baskets are hand-made and must be ordered far in advance of the holiday season at a cost of $8 each. The plan is to fill each basket with an assortment of readily available items, which the two of you will buy on demand upon securing each order. The average cost of a basket's contents is $73. The unit selling price of a gift basket will be $100. The basket supplier has agreed to buy-back any leftover empty baskets for $2 each at the end of the season. Demand for gift baskets is random with the following discrete distribution:

Total number of gift baskets demanded. Probability

5 .07

10 .13

15 .10

20 .15

25 .10

30 .15

35 .15

40 .10

45 .05

(a) What is the marginal cost of shortage?

(b) What is the marginal cost of excess?

Explanation / Answer

Total cost of basket along with the content C = $ 8 + $73 = $81

Selling price of gift basket = P = $100

Salvage value of leftover basket = S = $2

Thus ,

Marginal cost of shortage = Cost of underage = P – C = $100 - $81 = $19

Marginal cost of excess

= Cost of overage

= Original purchase price of basket/ unit – Buy back price of empty baskets = $8 - $2 = $6

Thus ,

Critical ratio = Cu / ( Cu + Co) = 19/ ( 19 + 6) = 19/25 = 0.76

Critical ratio will correspond to the probability of minimum demand quantity i.e. number of baskets which should be ordered.

Following table illustrates probability of minimum demand quantities at different levels .

Probability that demand will be minimum this quantity

Probability

0.93

0.80

0.70

0.55

0.45

0.30

0.15

0.05

Since critical ratio of 0.76 is in between probabilities of 0.80 and 0.70 for 15 and 20 units respectively, ideally demand should be in between 15 and 20 and that should be =15 + ( 20 – 15)/ ( 0.80 – 0.70) x ( 0.76 – 0.70) = 15 + 3 = 18

Thus,

NUMBER OF EMPTY BASKETS TO BE ORDERED IN ADVANCE WILL BE 18 BASKETS

( Note: However if the condition is that empty baskets can be ordered in multiples of 5 in numbers as mentioned in the problem , we shall go for ordering 15 baskets since critical ratio value of 0.76 is nearest to the probability of 0.80 for quantity 15)