XYZ is a paint product manufacturer,and one of the plants is experiencing a substantial increase in demand.The future demand for the products could be low,medium,or high,with probabilities estimated to be 25%,50%,and 30%,respectively.The company wants to determine the financial impact associated with the three decision alternatives under the varying levels of demand.Given the following payoff matrix,compute the expected regret for the option of subcontracting additional capacity. $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Demand }$

$\begin{array} { | c | c | c | c | }
\hline \text { Decision Aternative } & \text { Low } ( 20 \% ) & \text { Medium } ( 50 \% ) & \text { High (30\%) } \
\hline \begin{array} { c }
\text { Subcontract additional } \
\text { capacity }
\end{array} & \$ 7 \text { million } & \$ 40 \text { million } & \$ 70 \text { m illion } \
\hline \text { Build a new plant } & - \$ 55 \text { million } & \$ 25 \text { million } & \$ 100 \text { million } \
\hline \text { Do nothing } & \$ 15 \text { million } & \$ 30 \mathrm {~m} \text { illion } & \$ 85 \text { million } \
\hline
\end{array}$
A)$10.6 M
B)$21.5 M
C)$9.5 M
D)$14 M

Question

XYZ is a paint product manufacturer,and one of the plants is experiencing a substantial increase in demand.The future demand for the products could be low,medium,or high,with probabilities estimated to be 25%,50%,and 30%,respectively.The company wants to determine the financial impact associated with the three decision alternatives under the varying levels of demand.Given the following payoff matrix,compute the expected regret for the option of subcontracting additional capacity. $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Demand }$

$\begin{array} { | c | c | c | c | } 
\hline \text { Decision Aternative } & \text { Low } ( 20 \% ) & \text { Medium } ( 50 \% ) & \text { High (30\%) } \
\hline \begin{array} { c } 
\text { Subcontract additional } \
\text { capacity }
\end{array} & \$ 7 \text { million } & \$ 40 \text { million } & \$ 70 \text { m illion } \
\hline \text { Build a new plant } & - \$ 55 \text { million } & \$ 25 \text { million } & \$ 100 \text { million } \
\hline \text { Do nothing } & \$ 15 \text { million } & \$ 30 \mathrm {~m} \text { illion } & \$ 85 \text { million } \
\hline
\end{array}$
A)$10.6 M
B)$21.5 M
C)$9.5 M
D)$14 M

Quizplus · Accepted Answer

The expected regret for the option of subcontracting additional capacity is $10.6 million. This is calculated by taking the difference between the payoff for the best decision alternative under each demand level and the payoff for the subcontracting decision alternative under each demand level, and then multiplying by the probability of each demand level. The expected regret is then the sum of these products.For example, the expected regret for the low demand level is $7 million - $15 million * 0.25 = $2.5 million. The expected regret for the medium demand level is $40 million - $30 million * 0.50 = $5 million. The expected regret for the high demand level is $70 million - $85 million * 0.30 = $3.1 million. The expected regret is then $2.5 million + $5 million + $3.1 million = $10.6 million.

XYZ Is a Paint Product Manufacturer,and One of the Plants \quad

XYZ Is a Paint Product Manufacturer,and One of the Plants $\quad$