Formulate and solve this problem as a binary programming problem.
Kloos Industries has projected the availability of capital over each of the next three years to be $850,000, $1,000,000, and $1,200,000, respectively. It is considering four options for the disposition of the capital:
a. Research and development of a promising new product
b. Plant expansion
c. Modernization of its current facilities
d. Investment in a valuable piece of nearby real estate
Monies not invested in these projects in a given year will NOT be available for the following year's investment in the projects. The expected benefits three years hence from each of the four projects and the yearly capital outlays of the four options are summarized in the table below in millions of dollars.
In addition, Kloos has decided to undertake exactly two of the projects. If plant expansion is selected, it will also modernize its current facilities.
Max 5.2X1 + 3.6X2 + 3.2X3 + 2.8X4
s.t. 0.35X1 + 0.50X2 + 0.35X3 + 0.50X4 ? 0.85 (Year 1)
0.55X1 + 0.50X2 + 0.40X3 ? 1.00 ( Year 2)
0.75X 1 + 0.45X3 ? 1.20 (Year 3)
X1 + X2 + X3 + X4 = 2
X2 + X3 ? 0
Xi = 0 or 1
X1 = 1, X2 = 0, X3 = 1, X4 = 0, total projected benefits = $8.4 million
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