Problem $4.$ Construction Method Selection $(25$ marks$)$

You are the production manager for a very large construction company that is about to start a major

concrete pour that is estimated to last for $10$ days. Your primary job during this time is to provide the

necessary forms each day:

To meet these requirements, you have three options: $1)$ you can purchase new forms for $$200$

each; $2)$ you can recondition used forms using a standard process that takes $4$ days and costs $$25$ per form;

or $3)$ you can recondition forms using a special $$fast$$ process that takes $2$ days and costs $$75$ each. Assume

that the company supplying you with forms has sufficient inventory to supply all new forms if necessary.

Also, you have no forms prior to the start of this operation.

Formulate a linear program that will suggest a strategy for meeting the demand for forms at least

total cost.