Down Chemicals manufacturers three chemicals: A, B and C. These chemicals are produced via 2 production processes: 1 and 2. Running process 1 for a month costs $40,000/run and yields 30,000 units of A, 10,000 units of B and 10,000 units of C. Running process 2 for a month costs $10,000/run and yields 10,000 units of A and 10,000 units of B. To meet the customer demand, at least 100,000 units of A, 50,000 units of B and 30,000 units of C must be produced on monthly basis. The firm also has incurs an additional cost to purchase the ingredients for the chemicals. The cost of ingredients for A, B and C are $2, $1 and $1 respectively per unit.

1. Find the monthly production plan.

Suppose Down Chemicals faces yield uncertainty in relation to Process 1; in particular, the yield can be 80%, 90%, 100%. For example, when the yield is 80%, only 80% of the chemicals that are produced through process 1 are useable. Each of these cases are equally likely. Due to long lead times associated with procurement, Down has to buy the ingredients in advance before it has any information regarding the yields of the processes. In addition, because of regulatory considerations, any unused ingredients would also have to be written off and cannot be used in any future production processes.

2. What is the new production plan.

3. Down, after examining its processes, realizes that the exact yield associated with its processes can be determined if it were to conduct a thorough quality check. What is the maximum value that they should spend on this quality check, given that they can make their procurement decision after the quality checks?