Before we can determine the expected cost of using one of the machines, we first need to calculate the expected demand. This is done by multiplying each of the possible demands by the probability of that demand occurring and then adding the numbers together to calculate a weighted average, or expected value. The expected demand is 300,000 units, calculated as [(200,000 × .4) + (300,000 × .3) + (400,000 × .2) + (500,000 × .1)]. Now, putting the expected value of the demand of 300,000 into the formula for the semi-automatic machine, we get an expected cost of $170,000 [(300,000 × $.40) + $50,000].
$210,000 is the expected cost of using the semi-automatic machine if demand at the probability level of 0.2 (400,000 units) is used.
$130,000 is the expected cost of using the semi-automatic machine if demand at the highest level of probability (demand of 200,000 units; probability 0.4) is used.
250,000 is the expected cost of using the semi-automatic machine if demand at the probability level of 0.1 (500,000 units) is used.
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Ignoring the time value of money, the expected cost of using the semi-automatic machine is