Question 4: Product Mix Design (30 points) The R&D department of a company has developed three new products: now they want to decide on the best mix to produce. Management considers three goals: total discounted prot over the life of these products (P), stability regarding the current level of employment (S) and an increase of the company's earnings in the next year (E). After assigring weights to these objectives, management's goal is to maximize the following objective function: Z = 5P 2{S+ S') 3E'. Here 8+ and S" denote deviations from the current level of employment (both being equally penalized), and E" denotes a negative deviation from next year's earning target. The unit contributions of the new products to the objectives considered are shown below. Factor Goal Unit: Total Prot Maximize Millions of dollars Enmloyment Level = 50 Hundreds of on'ployoes Earnings next year a 7'5 Millions of dollars Develop a goal programing LP model in Excel to support the company's decision and solve it using Solver. Interpret your results. Feel free to add your own comments regarding the model and its possible extensions