The ABC Cement Corporation produces a high quality cement that is supplied to construction companies.The potential demand and the probability of each potential demand quantity are given for the upcoming year. $$\begin{array} { | c | c | }
\hline \text { Dernand in tons } & \text { Probability } \
\hline 500,000 & 0.3 \
\hline 250,000 & 0.4 \
\hline 300,000 & 0.3 \
\hline
\end{array}$$ Assuming manufacturing capacity of 700,000 tons,the estimated capacity cushion is:

Question

The ABC Cement Corporation produces a high quality cement that is supplied to construction companies.The potential demand and the probability of each potential demand quantity are given for the upcoming year. $$\begin{array} { | c | c | } 
\hline \text { Dernand in tons } & \text { Probability } \
\hline 500,000 & 0.3 \
\hline 250,000 & 0.4 \
\hline 300,000 & 0.3 \
\hline
\end{array}$$ Assuming manufacturing capacity of 700,000 tons,the estimated capacity cushion is:

Quizplus · Accepted Answer

The capacity cushion is the difference between the manufacturing capacity and the expected maximum demand. The expected maximum demand is the demand with the highest probability, which is 500,000 tons. Therefore, the estimated capacity cushion is:

700,000 - 500,000 = 200,000 tons

However, this capacity cushion is based on the expected maximum demand, which has a probability of only 0.3. There is also a probability of 0.4 for a demand of 250,000 tons and a probability of 0.3 for a demand of 300,000 tons. Therefore, we need to calculate the capacity cushion for each possible demand and multiply it by its probability. Then we can add these results to get the expected capacity cushion:

(700,000 - 500,000) x 0.3 + (700,000 - 250,000) x 0.4 + (700,000 - 300,000) x 0.3
= 60,000 + 180,000 + 120,000
= 360,000

Therefore, the estimated capacity cushion is 360,000 tons.

The ABC Cement Corporation Produces a High Quality Cement That