Each full share of Venture 1 requires an investment of $1,000, and proportional amounts are required for fractional shares. By contrast, Venture 2 requires no investment and instead provides an advance of $1,000 per share (or proportionally for fractional shares) in return for the work commitment that accompanies shares of this venture.

Leo has savings of $1,000 available for investment. The advance from Venture 2 also will arrive in time for any desired investment in Venture 1. Shares in either venture include a time commitment, so Leo must work an average of 3 hours per day for each share of Venture 1 and 1 hour per day for each share of Venture 2, with proportional commitments for fractional shares. He is willing to work a maximum of 7 hours per day on the average.

Both ventures should provide Leo with substantial net earnings when he sells out to return to college. He estimates that he can increase his current savings by $20,000 per share of Venture 1 and $10,000 per share of Venture 2. Leo's objective is to maximize his savings for returning to college. He wants to know how many shares of each of these ventures he should take in order to accomplish this objective. Let us see how linear programming and its graphical method can solve this problem.