© 2000 John Petroff

7)- Linear programming application

Linear programming was outlined in Chapter 5. We will proceed to the formulation of the problem. The objective function states that the combination of NPV's of the remaining projects (p₁, p₂, p₆, p₇ and p₈) must maximize owner's wealth W.

Maximize W = 25.16p₁+ 7.74p₂ + 1.41p₆ + 73.56p₇ + 47.76p₈

 Subject to the following constraints:

The first constraint is that the sum of initial outlays must be smaller than the available borrowing limit of $ 2.500 millions less the purchase of one truck for $ 30,000 of project 4.

1450p₁ + 200p₂ + 35p₆ + 500p₇ + 500p_{8 £} 2,470

The remaining constraints are that the total cash flow in each year must be positive.

200p₁ + 30p₂ + 10p₆ + 100p₇ + 5p_{8 ³} 0

200p₁ + 30p₂ + 10p₆ + 150p₇ + 15p_{8 ³} 0

:

200p₁ + 30p₂ + 10p₆ - 300p₇ + 100p_{8 ³} 0

The system of equation is solved by determining which p₁ through p₈ variables have values of 1 or 0.

In our example, the solution turns out to be very straight forward with the rejection of p₂ and p₆ , and acceptance of three projects ( p_1, , p₇ and p₈ ), plus project p₄ which had to be accepted a priori. The total NPV for the four retained projects is $ 146,480. For more complex examples of linear programming and constrained optimization, one should consult operations research manuals.

See review questions Q-10E7.1 through Q-10E7.3.

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Last modified: Jun/01/01

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