Question

The Supermarket Store is about to place an order for Halloween candy. One best-selling brand of candy can be purchased at $2.40 per box and usually is sold for $6 per box before and up to Halloween. After Halloween, all the remaining candy can be marked down and sold for $1.00 per box. Assume that the loss in goodwill “cost” stemming from customers whose demand is not satisfied is $0.30. Demand for the candy at the regular price is a random variable with the following discrete probability distribution:

Demand (boxes)	Probability
80	0.05
90	0.45
100	0.10
110	0.25
120	0.15

i. Eliminate the possibility of have any leftover candy at the end of the selling season by ordering 80 boxes;

ii. Eliminate the possibility of not losing any sales through inadequate stock by ordering 120 boxes.

^For each of the above options, you are required to estimate the expected (end-of-season) profits for the supermarket store.

b. If the store manager’s objective is to obtain the maximum end-of-season expected profit for the store, what would be:

• the optimal order quantity (Q*); and

• the corresponding expected profit?

**Please show work

Answer 1

The expected profit for any quantity ordered =

$6*(min (ordered, demand))-$2.40*ordered +1*(Ordered-Demand)+ - 0.30 (demand-Ordered)+

Here the first part is the sales revenue which takes into account the minimum of demand or order.

The second part is the cost of ordered units

The third part is the leftover quantity. This superscript plus sign shows it is always a positive value and if the order is less than demand it is zero

The fourth part is the goodwill loss cost which dissimilar to above i.e. if demand is less than order it is zero

The excel calculation with formulae is shown below

i) If we order 80 units then we can expect a profit of 282

ii) If we order 120 units then we can expect a profit of 332

According to the above excel calculation the , the maximum expected profit we can get is 338.05 and by ordering 110 units

Q*= 110 units

Expected profit = 338.05

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