Formulate an optimisation model that determines the profit-maximising production mix.

The R&D Division of the Progressive Company has been developing four possible new product lines. The board of the company must now make a decision as to which of these four products actually will be produced and at what levels. A substantial cost is associated with beginning the production of any product, as given in the first row of the following table. The company has already undertaken a market research, which has led to estimates of the maximum demand for each product (third row). Assume that the company wants to find the product mix that maximises the total profit (i.e., the total net revenues (using the unit revenues from the second row) minus the start-up costs). Product line 1 2 3 4 Start-up costs 50,000 40,000 70,000 60,000 Net revenues/unit sold 70 60 90 80 Maximum demand (units) 10,000 15,000 12,500 9,000 Moreover, the production plan is restricted by the following considerations: 1. At most two of the product lines should be produced. 2. Product 1 can only be produced if either product 2 or product 3 (or both) is produced. 3. Either the cumulative production quantities of products 1 and 3 are less than or equal to 20,000, or the cumulative production quantities of products 2 and 4 are less than or equal to 20,000 (or both). (a) Formulate an optimisation model that determines the profit-maximising production mix. Make sure you explain your model! (b) Solve your model using Excel. What is the profit-maximising production mix? (c) The Progressive Company is worried that some of their considerations 1, 2 and 3 may be too restrictive. What would you tell the board members