Problem 8: Clarke Corporation manufactures three products (X1,X2, and X3) 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. Required: a. 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? e. A local engineering firm claims it can revise the production process such that product X2 only requires 1.6 machine hours on the shared machine. How much would Clarke be willing to pay per period for the new process