7. Selecting Projects. The Texas Electronics Company (TEC) is contemplating a research and development program encompassing eight major projects. The company is constrained from embarking on all projects by the budget available for projects {$300,000}. Following are the resource requirements and the estimated profit for each project: ----mm man man\" a. What is the maximum profit, and which projects should be selected? b. Suppose that management decides that projects 2 and 3 are mutually exclusive. (In other words, TEC will not undertake both}. What is the revised project portfolio and the revised maximum profit? c. Suppose that management also decides to undertake at least two of projects 5-8. As a result, what are the revised project portfolio and maximum profit? (Assume b. is also true) Hint: In Excel, create different tabs for part a., b, and c.. Solve independently of each other. 8. Establishing a Product Line. National Metals Company {NMC} manufactures titanium shafts. Its equipment is capable of producing shafts in 10 lengths (in cm} as shown in the chart below, reflecting settings on its machinery. Setting up the machinery to produce one of these results costs $250. As a result, NMC has decided to make only a selected number of lengths. When a customer requests a given length, NMC may supply it from stock, if it happens to match one of the lengths in the production schedule. Otherwise, NMC trims a longer length to meet the order. The variable cost for producing the shafts is $20 per cm, and NMC receives revenue of $40 per cm. Trim waste can be sold to a recycler for $15 per cm. The demand requirements for the coming week are tabulated as follows; all demand must be satisfied. Iii-m1.- mm.\" d a. What is the optimal assortment of lengths for NMC to manufacture? b. What is the ootimal profit in the coming week