Decision 150 175 200 225 250 EXPECTED
160 16300 17600 17600 17600 17600 17535
180 15900 19150 19800 19800 19800 19507.5
200 15500 18750 22000 22000 22000
220 15100 18350 21600
Probabilities 0.05 0.15 0.4 0.3 0.1
The reasoning behind these numbers is as follows. You have to make a decision to order a certain number of items,
and there is a demand for these products. For example let's take a look at the first cell in the table.
Let's say that you take the decision to order 160 items, and the demand was 150 items.
We know from the statement of the problem that during the regular season you can sell the items at $260 and your
cost was $150, therefore your profit is $110 dlls per item.
If you order 160 items and your demand was 150 items you sold 150 items at full price, and your profit was $110 x
150 = $16,500
However, you were left with 10 items that were not sold because the demand was lower than your order, these
items have to be sold at the end of the season at a discounted price of $130, therefore because your cost was $150,
you loose $20 for each item sold at the end of the season. These 10 items have to be sold at that price, then your
lose is 10 items x $20/item = $200.
Your profit for this combination of ordering 160 items when the demand was 150 items was
= $ 16,500 - $200 = $16,300
As you can see from the table that I provided,
A different situation happens when the demand exceeds your order, in that case you can't sell more items than the
ones that you ordered, therefore for the case when the demand was 175 items and you ordered 160, your profit is
160 items x $110 = $17,600 and no lose. The rest of that row is the same, because if the demand is 200 items or 225
items, you still can't sell more than 160 and therefore your profit remains the same.
Problem 12 is very similar. If you understand this example you should be able to work on problem 12,
certain number of items,
he items at $260 and your
d your profit was $110 x
than your order, these
cause your cost was $150,
at that price, then your
t sell more items than the
rdered 160, your profit is
emand is 200 items or 225