A. The expected demand is 300,000 units [(200,000 × .4) + (300,000 × .3) + (400,000 × .2) + (500,000 × .1)]. The automatic machine has an expected cost of $180,000 [(300,000 × $.20) + $120,000], which is not the lowest expected cost.

B. The expected demand is 300,000 units [(200,000 × .4) + (300,000 × .3) + (400,000 × .2) + (500,000 × .1)].

The single purpose machine has an expected cost of $200,000 [(300,000 × $.60) + $20,000], which is not the lowest expected cost.

C. The expected demand is 300,000 units [(200,000 × .4) + (300,000 × .3) + (400,000 × .2) + (500,000 × .1)]. This question requires us to determine the cost of all of the machines at a level of 300,000 units. For the semi-automatic machine, we get an expected cost of $170,000 [(300,000 × $.40) + $50,000]. The single purpose machine has an expected cost of $200,000 [(300,000 × $.60) + $20,000] and the automatic machine has an expected cost of $180,000 [(300,000 × $.20) + $120,000]. The semi-automatic machine has the lowest expected cost and therefore should be used.

D. The expected demand is 300,000 units [(200,000 × .4) + (300,000 × .3) + (400,000 × .2) + (500,000 × .1)]. The automatic machine has an expected cost of $180,000 [(300,000 × $.20) + $120,000], which is not the lowest expected cost.