bria o=- Styles Text Box 5l Problem 4 (12 points) The Welsh Rabbit is a retailer

Question

bria o=- Styles Text Box 5l Problem 4 (12 points) The Welsh Rabbit is a retailer of European cheese and related products. In one of their local stores they plan to offer a gift basket of cheese, crackers, and tea for the holiday season. They plan to place one order for the gift baskets, and any leftover inventory will be discounted at the end of the season. Expected demand for the gift baskets at this location is 4.5 baskets, Poisson-distributed. The gift basket sells for $55, the purchase cost to The Welsh Rabbit is $32, and leftover baskets will be sold at 40% of the original price (60% on suppose they purchase only 3 gift baskets what is the probability that some demand will not be satisfied? b. Stppose they purchase 10 gift baskets. What is the expected left over inventory? 0010424 1% probability so all baskets are leftover? c. Suppose they purchase 4 baskets. How many baskets can they expect to sell? d. How many baskets should The Welsh Rabbit purchase to maximize the expected profit? What is the expected profit for that order quantity? |DE EI Print Layout View Sec 1 Pages: 100%-- O NOV 30

Explanation / Answer

(a) the demand/ sale of baskets are poisson distributed with = 4.5 baskets

They purchase only 3 baskets. So, some demand will not be satisfied if demand is more than 3 basket on any given day.

Let say the demand is X on any perticular day.

so Pr(X > 3) = POISSON (X > 3; = 4.5) = 0.6577

(b) They purchase 10 gift baskets. Expected left over inventory.

as Pr(X < = 10) = POISSON (X < = 10 ; 4.5) = 0.9933

so it can be assumed as that at maximum 10 baskets the demand.

Expected left over inventory = Purchased Basket - Expected demand = 10 - 4.5 = 5.5

c. Purchaed 4 baskets. Expected number of basets they would be able to sell.

Expected bskets they would be able to sell = Probability of selling that number of basket * That number of basket

= Pr(X = 0) * 0 + Pr(X =1) * 1 + Pr( X =2) * 2 + Pr(X = 3) * 3 + [1 - Pr(X = 0,1,2,3)] * 4

= 0.0111 * 0 + 0.05 * 1 + 0.1125 * 2 + 0.1687 * 3 + 0.6577 * 4

= 3.412

so the company would expect to sell 3.412 baskets.

(d) Here Wholesale cost w = $32

Selling price = $ 55

Leftover price = 55 * 0.4 = $ 22

Here overage cost = c -s = $32 - $22 = $ 10

underage cost = p - c = $ 55 - $ 32 = $ 23

Pr(do not sell Q + 1nd cost) = 23 / (10 + 23) = 0.69697

so if X is the number of baskets that must be purchased .

then Pr(X < x ) = POISSON (x < X ; 4.5) = 0.69697

as per poisson pdf

for X = 5; Pr(X =< 5 ; 4.5) = 0.7029

so yes the company must purchase 5 units of basket.

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