The PPE Company is considering three new products to replace current models that are being discontinued

The PPE Company is considering three new products to replace current models that are being discontinued. Their OR department has determined which mix of these products should be pro- duced. Management wants consideration to be given to three factors that would be required for new equipment: long-run profit, stability in the workforce, and the level of capital investment. Management has established the goals of (a) achieving a long-run profit (net present value) of at least R125 million from these products (b) maintaining the current employment level of 4000 employees (c) holding the capital investment to less than R55 million. However, management realises that it probably will not be possible to attain all these goals simul- taneously, so it has discussed priorities with the OR department. This discussion has led to the setting of the following penalty weights: • 5 for missing the profit goal • 2 for going over the employment goal of 4000 employees • 4 for employing less than the 4000 employees . 3 for exceeding the capital investment goal. Each new product's contribution to profit, employment level and capital investment level is pro- portional to the rate of production. These contributions per unit rate of production are shown in the table. Product A B C Long-run profit Employment level Capital investment (in million rand) ('00 employees) (in million rand) 12 5 5 9 3 7 15 4 8 Formulate the problem but do not solve it.