 # a. Find Carolina's monthly order quantity for the product if the company bases m Charles Cisneros 2021-11-20 Answered
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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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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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.