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 value of decisions with perfect information. $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Demand }$

$\begin{array} { | c | c | c | c | }
\hline \text { Decision Altemative } & \text { Low(20\%) } & \text { Medium(50\%) } & \text { High (30\%) } \
\hline \begin{array} { c }
\text { Subcontract additional } \
\text { capacity }
\end{array} & \$ 7 \text { million } & \$ 40 \text { million } & \$ 70 \text { million } \
\hline \text { Build a new plant } & - \$ 55 \text { million } & \$ 25 \text { million } & \$ 100 \text { million } \
\hline
\end{array}$

A)$45.5 M
B)$53M
C)$12.4 M
D)$70 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 value of decisions with perfect information.  $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Demand }$

$\begin{array} { | c | c | c | c | } 
\hline \text { Decision Altemative } & \text { Low(20\%) } & \text { Medium(50\%) } & \text { High (30\%) } \
\hline \begin{array} { c } 
\text { Subcontract additional } \
\text { capacity }
\end{array} & \$ 7 \text { million } & \$ 40 \text { million } & \$ 70 \text { million } \
\hline \text { Build a new plant } & - \$ 55 \text { million } & \$ 25 \text { million } & \$ 100 \text { million } \
\hline
\end{array}$

A)$45.5 M
B)$53M
C)$12.4 M
D)$70 M

Quizplus · Accepted Answer

To calculate the expected value of decisions with perfect information (EVwPI), we first determine the maximum payoff for each demand scenario, then multiply each by its probability and sum them up. For low demand, the maximum payoff is $7 million (from subcontracting), for medium demand, it's $40 million (from subcontracting), and for high demand, it's $100 million (from building a new plant). The probabilities given in the question are incorrect as per the matrix, so we'll use the corrected probabilities from the matrix: Low (20%), Medium (50%), High (30%).EVwPI = (0.25 * $7M) + (0.50 * $40M) + (0.30 * $100M) = $1.75M + $20M + $30M = $51.75M.However, there seems to be a discrepancy in the probabilities provided in the text versus those in the matrix. Assuming the probabilities in the matrix are the correct ones to use (20%, 50%, 30%), the calculation should actually be based on these. But given the options and the initial mistake in the question setup, we proceed with the probabilities as 25%, 50%, and 30% for consistency with the provided options, acknowledging the error in the demand probabilities.Correcting for the intended probabilities (25%, 50%, 30%) and the calculation mistake:EVwPI = (0.25 * $7M) + (0.50 * $40M) + (0.30 * $100M) = $1.75M + $20M + $30M = $51.75M.Given the options, none directly match this corrected calculation, suggesting a potential error in the question or in the interpretation of the probabilities and options provided. The closest option to the corrected calculation is $53M, which might be chosen due to rounding or a minor calculation error in the question setup.

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

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