A Plant Manager Is Considering Buying Additional Stamping Ma ✓ Solved
A Plant Manager Is Considering Buying Additional Stamping Machines To
A plant manager is evaluating options for acquiring additional stamping machines to meet increasing production demands. The decision involves three alternatives: purchasing one machine, two machines, or three machines. The profitability of each alternative depends on whether a recent defense contract bid is accepted or rejected. The payoffs, expressed in thousands of dollars, are provided in the following table:
| Alternative | Bid Accepted | Bid Rejected |
|---|---|---|
| Buy 1 machine | $10,000 | $5,000 |
| Buy 2 machines | $30,000 | $4,000 |
| Buy 3 machines | $40,000 | $2,000 |
Applying the Laplace Criterion to the Decision-Making Process
The Laplace criterion, also known as the principle of insufficient reason, assumes that all future states of nature are equally likely. Therefore, it recommends choosing the alternative with the highest average payoff, computed under the assumption that each state occurs with equal probability. In this context, the two scenarios—bid accepted and bid rejected—are considered equally probable, each with a probability of 0.5.
Calculating the Expected Payoff for Each Alternative
To determine the optimal choice under the Laplace criterion, we first calculate the expected payoff for each alternative by averaging the payoffs associated with the bid accepted and rejected scenarios.
Expected Payoff for Buying One Machine
Expected payoff = (0.5 × $10,000) + (0.5 × $5,000) = $5,000 + $2,500 = $7,500
Expected Payoff for Buying Two Machines
Expected payoff = (0.5 × $30,000) + (0.5 × $4,000) = $15,000 + $2,000 = $17,000
Expected Payoff for Buying Three Machines
Expected payoff = (0.5 × $40,000) + (0.5 × $2,000) = $20,000 + $1,000 = $21,000
Decision Based on the Laplace Criterion
Comparing the expected payoffs, we observe that purchasing three machines yields the highest expected profit of $21,000. Therefore, according to the Laplace criterion, the optimal decision for the plant manager is to buy three stamping machines.
Conclusion
By assuming equal probabilities for the success or failure of the defense contract bid, the plant manager can maximize expected profits by opting for the purchase of three machines. This decision aligns with the principles of the Laplace criterion, prioritizing the choice with the highest average payoff across all scenarios.
References
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