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# I need help answering A-D below

Im stuck on a Management question and need an explanation.

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• HKV Company is considering investing in several projects that have varying capital requirements over the next four years. The net present value of each project, cash outflows required over the years and capital available per year are given (in millions) in the table below:
 Plant 1 Expansion Plant 2 Expansion New Product Development Automation Annual Capital Available Year 1 8 5 4 7 20 Year 2 10 7 2 5 25 Year 3 10 10 1 5 20 Year 4 7 3 1 5 15 NPV of each Project 45 20 10 20

Each project must be done in full (with the corresponding cash flows for all the years) or not done at all. Any available money not spent in a given year is then available to spend the following year. Help the company find the optimal investment plan that would maximize the total net present value. (Recall the Capital Budgeting example in Section 3.2. There are some similarities between the example and this problem, but some differences  this is a BIP problem.)

• (A)Formulate the problem as a binary integer programming (BIP) problem in spreadsheet form. Solve the spreadsheet model. What is the optimal investment plan? What is the total net present value of the optimal investment plan
• (B)Additional constraint is considered: the New Product Development is selected only if Plant 2 Expansion project is also adopted. Formulate and solve the spreadsheet model. What is the optimal investment plan? What is the total net present value of the optimal investment plan
• (C) From question b, considering one more constraint: Plant 1 Expansion and Plant 2 Expansion cannot be both selected. Formulate and solve the spreadsheet model. What is the optimal investment plan? What is the total net present value of the optimal investment plan?
• (D)Formulate the problem (b) as a binary integer programming (BIP) problem in algebraic form.