A fisherman is considering expansion of his operations. He has the opportunity to purchase a new fishing boat and net licence, to set up an on-shore fish processing depot and to build a fish canning operation. His current scale of operation does not warrant setting up the processing plant. The canning operation cannot proceed unless on-shore processing is carried out. The net present values for the three projects are $$\$ 2 \mathrm{M}$$, $$\$ 1 \mathrm{M}$$ and $$\$ 1.5 \mathrm{M}$$. Year 1 and year 2 capital outlays for the new boat and licence are $$\$ 400,000$$ and $$\$ 200,000$$, for the processing plant $$\$ 300,000$$ and $$\$ 300,000$$, and for the canning plant $$\$ 200,000$$ and $$\$ 300,000$$. The fisherman has $$\$ 800,000$$ in cash reserves, and can borrow money in years 1 and 2 , of up to $$\$ 1 \mathrm{M}$$ in total, at a $12 \%$ interest rate. Set up these investment opportunities as a linear programming model, and determine the optimal investment portfolio.