Problem 3. Designer Assignment (25 marks) A small engineering consulting firm has 3 senior designers available to work on the firm's 4 current projects over the next 2 weeks. Each designer has 80 hours to split among the projects, and the following table shows the manager's evaluation (\(0=\) nil to \(10=\) perfect) of quality performance of each designer to contribute to each project, along with his estimate of the hours that each project will require. The manager wants to assign designers to maximize the overall quality performance. Formulate a mathematical program to choose an optimal work assignment. 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.