Three Different Designs Are Being Considered for a New Refrigerator

question 47

Essay

Three different designs are being considered for a new refrigerator, and profits will depend on the combination of the refrigerator design and market condition. The following payoff table summarises the decision situation, with amounts in millions of dollars. $\begin{array} { ccc }&\text { Alternative }\\\text { State of Nature }& a_{1} & a_{2} & a_{3}\\\text { (Market condition) }\\s_{1} & \$ 30 & \$ 20 & \$ 10 \\s_{2} & \$ 19 & \$ 21 & \$ 15 \\s_{3} & \$ 11 & \$ 23 & \$ 35\end{array}$
Assume that the following probabilities are assigned to the three market conditions:
P( $S _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.4, P( $S _ { 3 }$ ) = 0.4.
a. Calculate the expected monetary value for each design with present information. Which design should be selected in order to maximise the firm's expected profit?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each design with present information. Which design should be selected in order to minimise the firm's expected loss?
d. Determine the expected payoff that would be realised if perfect information were available.
e. What is the most the firm would be willing to pay for a research study designed to reduce its uncertainty about market conditions?

---

Definitions:

Projected Hurricanes

Forecasted tropical cyclones that are expected to develop into hurricanes based on meteorological data.

Product Offerings

The range of products or services that a company makes available for customers.

Survival Kits

Pre-assembled packages containing essential items and tools intended to aid survival in emergency situations or disasters.

Emergency Supplies

Items and resources stored in preparation for unexpected events or disasters to ensure survival and safety.