# a. Find Carolina's monthly order quantity for the product if the company bases m

a. Find Carolina's monthly order quantity for the product if the company bases monthly orders on the expected value of the monthly demand.
b. Find the company's gain or loss in a month if it places an order based on the answer to part (a) and the actual demand for the item is 300 units.

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Provere
a. Calculation:
The data represents the probability distributions of company's monthly demand for the past two years.
The formula for the expected value of a discrete random variable is,
$$\displaystyle{E}{\left({x}\right)}=\mu$$
$$\displaystyle=\sum{x}\cdot{f{{\left({x}\right)}}}$$
The expected monthly order quantity is obtained using the following table:
\begin{array}{|c|c|} \hline x&f(x)&x \cdot f(x) \\ \hline 300&0.20&60 \\ \hline 400&0.30&120\\ \hline 500&0.35&175\\ \hline 600&0.15&90\\ \hline Total&1.00&445\\ \hline \end{array}
Thus, the monthly order quantity should be 445 units.
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pseudoenergy34
b. Calculation:
The assumption is that each unit demanded generates $70 in revenue and that each unit ordered costs$50.
It is expected that the monthly order quantity should be 445 units. Each unit ordered costs $50. Thus, the cost is calculated as, $$\displaystyle{445}\times\{50}=\{22},{250}$$. The actual demand for the item is 300 units and each unit demanded generates$70 in revenue. Thus the revenue is calculated as, $$\displaystyle{300}\times\{70}=\{21},{000}$$.
Here, the cost is greater than the revenue and the company has a loss of $$\displaystyle\{1},{250}{\left(=\{22},{250}-\{21},{000}\right)}$$ in a month if it places an order based on the answer to part (a) and the actual demand for the item is 300 units.