Consider the following problem. Our factory is building three products: TV sets, stereos and speakers. Each product is assembled from parts in inventory, and there are five types of parts: chassis, picture tubes, speaker cones, power supplies and electronics units. Our goal is to produce the mix of products that will maximize profits, given the inventory of parts on hand. The profit per unit of TV set, stereos and speakers is $60, $50 and $50, respectively. The number of chassis, picture tubes, speaker cones, power supplies and electronics available in inventory are 450, 250, 800, 450 and 600 units, respectively. The parts required by each product is provided in the table below. For example, a TV set requires one each of chassis, picture tube, and power supply and two each of speaker cone and electronics.
Based on the “Spreadsheet model” and “Sensitivity” reports provided below, answer the following questions. All answers have to be explained clearly. One word answers will not be sufficient.
- What is the optimal profit and optimal product mix (number of TV sets, stereos and speakers)?
- True or False (explain your answer): The total capacity of “chassis”, “picture tube” and “power supply” are completely used up.
- If the profit per unit of TV Set is changed to $80 (from the current $60) how does that affect the optimal profit mix and objective value? Explain your answer.
- Going back to the original problem and its solution, suppose that the manufacturer has located additional inventory of chassis from an external source at $ 20 per unit. How many additional chassis should they buy and how will this impact the total profit? Explain your answer.
- Going back to the original problem and its solution, suppose that the manufacturer has located 75 additional-inventory of speaker cones from an external source at $ 10 per unit. Should the manufacturer buy this and how will this impact the total profit?
- Going back to the original problem, if you have a budget of up to $2,000 to spend and the cost per unit of electronics is $20 in the open market, how much electronics would you buy? What will be the resulting impact on total profits of this expansion?
- Can you forecast the change to the optimal value if you bought 250 additional units of Electronics at $20 each? Explain your answer? Going back to the original problem, electronics are now in short supply in the regular market and you have to buy it in the black market? If it costs $30 per unit in the black market, would you buy it? If so, how many? If not, why not?
- What happens to the optimal product mix and profit if the profit associated with each speakers goes up to $60? Explain your answer.
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