Hart Venture Capital (HVC) specializes in providing venture capital for software development and Internet applications. Currently HVC has two investment opportunities: (1) Security Systems, a firm that needs additional capital to develop an Internet security software package, and (2) Market Analysis, a market research company that needs additional capital to develop a software package for conducting customer satisfaction surveys. In exchange for Security Systems stock, the firm has asked HVC to provide $600,000 in year 1, $600,000 in year 2, and $250,000 in year 3 over the coming three-year period. In exchange for their stock, Market Analysis has asked HVC to provide $500,000 in year 1, $350,000 in year 2, and $400,000 in year 3 over the coming three-year period. HVC believes that both investment opportunities are worth pursuing. However, because of other investments, they are willing to commit at most $800,000 for both projects in the first year, at most $700,000 in the second year, and $500,000 in the third year.

HVC's financial analysis team reviewed both projects and recommended that the company's objective should be to maximize the net present value of the total investment in Security Systems and Market Analysis. The net present value takes into account the estimated value of the stock at the end of the three-year period as well as the capital outflows that are necessary during each of the tree years. Using an 8% rate of return, HVC's financial analysis team estimates that 100% funding of the Security Systems project has a net present value of $1,800,000, and 100% funding of the Market Analysis project has a net present value of $1,600,000.

HVC has the option to fund any percentage of the Security Systems and Market Analysis projects. For example, if HVC decided to fund 40% of the Security Systems project, investments of 0.40($600,000) = $240,000 would be required in year 1, 0.40($600,000) = $240,000 would be required in year 2, and 0.40($250,000) = $100,000 would be required in year 3. In this case, the net present value of the Security Systems project would be 0.40($1,800,000) = $720,000. The investment amounts and the net present value for partial funding of the Market Analysis project would be computed in the same manner.

Perform an analysis of HVC's investment problem and prepare a report that presents your findings and recommendations. Include (but do not limit your discussion to) a consideration of the following items:

1. What is the recommended percentage of each project that HVC should fund and the net present value of the total investment?

2. What capital allocation plan for Security Systems and Market Analysis for the coming three-year period and the total HVC investment each year would you recommend?

3. What effect, if any, would HVC's willingness to commit an additional $100,000 during the first year have on the recommended percentage of each project that HVC should fund?

4. What would the capital allocation plan look like if an additional $100,000 is made available?

5. What is your recommendation as to whether HVC should commit the additional $100,000 in the first year?

Please, if possible, provide answers in a linear programming format.