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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

    x1 <= 1,000,000
    x1 - x2 <= 800,000
    x2 <= 0.4x1

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