You are the production manager for a large construction company that is about to start an important concrete pour, which is estimated to last 4 days. Your primary duty during that time is to provide the necessary forms each day, as given in the table below. To meet these requirements, you have 2 options: 1) you can purchase new forms for $150 each; or 2) you can recondition used forms using a process that takes 2 days and costs $50 per form (so recycled forms from day 1 are first available in day 3, and recycled forms from day 2 are first available in day 4). Assume that the company supplying you with forms has enough inventory to supply all new forms if necessary. Also, at the start of this job you do not have any used form to recycle.
Day 1 2 3 4
Number of forms needed: 30 55 80 70
a) Formulate a linear program that will give the optimum strategy for meeting the demand for forms at least cost. For full credit, clearly define your decision variables and label all your constraints.
b) Using your engineering judgment (not the simplex), what is the optimum solution?