# Linear Programming

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Finco must determine how much investment and debtto undertake during the next year. Each dollar invested reduces the NPV of the company by 10¢, and each dollar of debt increases the NPV by 50¢ (due to deductibility of interest payments). Finco can invest at most \$1 millionduring the coming year. Debt can be at most 40% of investment. Finco now has \$800,000 in cash available. Allinvestment must be paid for from current cash or borrowed money. Set up an LP whose solution will tell Finco how tomaximize its NPV.

• Linear Programming -

max z = .5x1 - .1 x2
s.t constraints
x2< = 1000000
x1<= 400000
x1 + x2 = 800,000

• Linear Programming -

x1 = amount invested
x2= amount borrowed

objective function:
Max = -0.10x1+0,5x2

s.t.:
x1 <= 1,000,000
x1 - x2 <= 800,000
x2 <= 0.4x1

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