A single product is purchased for a unit price of $ 10 and sold to the consumers for a profit of $ 3 per unit. The items that are not sold at the end of the period are returned to the supplier for a scrap value of $ 5 per unit.
The probability distribution of the demand for the product from the consumer is as
shown in the following table.
Demand, X 0 1 2 3 4 5 6 7 8
Prob. P(x) 0.05 0.1 0.1 0.2 0.25 0.15 0.05 0.05 0.05
Determine the optimal order quantity.