You have just joined Plato Ventures (PV), a technology venture capitalist (VC) specializing in high tech platform companies. The CEO of PV has directed you to evaluate 3 potential start-up platform companies for an investment program. The amount that PV has for this investment is $10 million ($10M). In addition, PV can only assign at most 600HRS of consulting manpower for these start-ups. Given the maturity of each start-up, the amount of capital and manpower commitments to invest by PV to maximize their success of these startups varies. All the start-ups are flexible and would agree to any fraction of the partnership commitments that were proposed by PV. However, the profits will be multiplied according to same fraction of capital and manpower invested. The proposed commitments and estimated profits for the 3 startups are as follows:

With the growing success of platform companies in the industry, PV CEOs directive is to invest the entire $10M of VC funds in these start-ups to maximize the profits.

(1) Formulate a linear programming model to determine the optimal fraction of capital and manpower to be allocated to each of the startup.

(2) Using graphical analysis, solve this linear programming model with the following:

a. Reformulate the LP if needed

b. Draw and label all the constraints.

c. Shade the feasible region in the graphical analysis and indicate redundant constraints.

Start-up 2 (SU2) $8M Start-up 3 (SU3) $5M Start-up 1 (SU1) Capital Investment | $10M by PV Manpower 400HRS Investment by PV Estimated Profit $9M 500HRS 300HRS $9M $7M Start-up 2 (SU2) $8M Start-up 3 (SU3) $5M Start-up 1 (SU1) Capital Investment | $10M by PV Manpower 400HRS Investment by PV Estimated Profit $9M 500HRS 300HRS $9M $7M