?Clarke Corporation manufactures three products (X-1, X-2, and X-3) utilizing, in one of the processes, a single machine for all products. Data on the individual products follow.

The single machine used for all three products has a maximum capacity of 500,000 hours per period.

Requireda. How many units of each product should be produced each period?b. A local engineering firm has suggested to Clarke that it might be able to increase the capacity on the machine. What is the maximum Clarke would be willing to pay for an increase of twenty (20) machine hours?c. Suppose the maximum capacity on the machine was 300,000 hours (instead of 500,000 hours). What is the maximum Clarke would be willing to pay for an increase of twenty (20) machine hours?d. At what capacity (in machine hours) would the machine no longer be a bottleneck?

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X-1 X-2 X-3 Price per unit Variable cost per unit Machine hours per unit Maximum units demand per period 100 $ 200 $ 400 50 $ 120 $ $ 240 1.0 2.5 4.0 300,000 150,000 20,000