Determine the expected cost of operating a large facility for two years, given the following information: Cost to build the large facility is $2 million. If demand is high (probabi... Determine the expected cost of operating a large facility for two years, given the following information: Cost to build the large facility is $2 million. If demand is high (probability 0.7), operating costs are $450,000 annually. If demand is low (probability 0.3), operating costs are $300,000 annually.
Understand the Problem
The question asks to calculate the expected operating cost of the large cross-dock facility over two years, considering the probabilities of high and low demand. This involves weighting the operating costs under each demand scenario by their respective probabilities and summing them.
Answer
$1,160,000
Answer for screen readers
$1,160,000
Steps to Solve
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Calculate the operating cost for high demand over two years. Given the annual operating cost for high demand is $700,000, the operating cost over two years is: $2 \times 700,000 = 1,400,000$
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Calculate the operating cost for low demand over two years. Given the annual operating cost for low demand is $400,000, the operating cost over two years is: $2 \times 400,000 = 800,000$
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Calculate the expected operating cost. The expected operating cost is calculated by weighting each scenario's cost by its probability and summing the results. The probability of high demand is 60% (0.6), and the probability of low demand is 40% (0.4).
Expected operating cost $ = (0.6 \times 1,400,000) + (0.4 \times 800,000) $ $ = 840,000 + 320,000 = 1,160,000 $
$1,160,000
More Information
The expected operating cost represents the average cost you would expect to incur over the two years, considering the probabilities of different demand scenarios. It's a weighted average that factors in both high and low demand possibilities.
Tips
A common mistake might be forgetting to multiply the annual operating costs by the number of years (2). Another mistake could be using the probabilities incorrectly or swapping them between high and low demand. Additionally, simple arithmetic errors when calculating the weighted costs can occur.
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