Problem:
The company needs to expand its production capacity. This can be done in one of two ways: using overtime in its current plant or leasing another plant. Overtime has a cost penalty (above regular time) of $3 per case of of product produced, and can only be used for up to 15,000 cases per year. Leasing another plant would entail an annual fixed leasing cost $25,000; however the workforce of this plant would be paid on a regular time basis and could produce any number of cases up to a maximum of 20,000 cases anually.
The company estimates that additional demand (beyond what can be produced in its current plant in regular time) may take on the following values, with corresponding probabilities:
Additional Demand (cases per year) Probability
5,000 .3
10,000 .5
15,000 .5
What is the optimal decision to minimize expected costs?