Don Robson, CEO for a public utility company in Ontario, has scheduled the const

Question

Don Robson, CEO for a public utility company in Ontario, has scheduled the construction of new hydroelectric plants 5, 10, and 20 years from now to meet the needs of the growing population. To cover the construction costs, Don needs to invest some of the company's money now to meet these future cash flow needs. Don may purchase only three kinds of financial assets, each of which costs $1 million per unit. Fractional units may be purchased. The assets produce income 5, 10, and 20 years from now, and that income is used to meet the cash flow needs. Data are shown below:

Explanation / Answer

We proceed to set up the following Linear Programming Problem.

Let x1, x2 and x3 be the number of units in each of the three financial assets.

The objective function is to minimize the current Cost. Each unit of the 3 assets cost $ 1M.
Thus, Z = Min { x1 + x2 + x3}

The constraints are provided by the minimum cash flows needed in years 5, 10 and 20.

Thus, 4x1 + 3x2 + 2 x3 >= 700

2x1 + 2x2 + 3x3 >= 400

x1 + 4x2 + 2x3 >= 600

x1, x2, x3 >= 0

The above are the constraints requested.

The above problem can be solved by the simplex method to obtain solutions.

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