Three Different Designs Are Being Considered for a New Refrigerator

question 50

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. $\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\\\text { (Market condition) }\\\begin{array}{ll}s_1\\s_2\\s_3\end{array}&\begin{array}{|lll|}\hline\$30\quad&\$20\quad&\$10\quad \\\$19&\$21&\$15\\\$11&\$23&\$35\\\hline\end{array}\end{array}$
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?

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Definitions:

Finished Goods Inventory

The stock of completed products ready for sale, reflecting the end-stage of the production process.

Value Chain

The major business functions that add value to a company’s products and services such as research and development, product design, manufacturing, marketing, distribution, and customer service.

Major Activities

The principal actions or operations carried out within an organization or by a project, typically contributing to achieving its main objectives.

Manufacturing Process

The sequence of operations or methods used to convert raw materials into finished goods.