Kloos Industries has projected the availability of capital over each of the next three years to...

 

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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: 1. research and development of a promising new product 2. plant expansion 3. modernization of its current facilities 4. 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. Options New product R&D Plant expansion Modernization Real estate Year 1 0.35 0.50 0.35 Capital Outlay 0.50 Year 2 0.55 0.50 0.40 0.00 Year 3 0.75 0.00 0.45 0.00 Projected Benefits 3.6 2.8 5.2 3.2 In addition, Kloos has decided to undertake exactly two of the projects. If plant expansion is selected, it will also modernize its current facilities. Formulate this problem as a binary programming problem in order to maximize projected benefits (in millions of dollars). (Let x; = 1 if project i is selected; 0 otherwise.) Max s.t. year 1 available capital year 2 available capital year 3 available capital exactly two projects constraint on plant expansion and modernization x₁ = 0, 1 Solve this problem. (X₁, X₂, X3, X₁) = 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: 1. research and development of a promising new product 2. plant expansion 3. modernization of its current facilities 4. 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. Options New product R&D Plant expansion Modernization Real estate Year 1 0.35 0.50 0.35 Capital Outlay 0.50 Year 2 0.55 0.50 0.40 0.00 Year 3 0.75 0.00 0.45 0.00 Projected Benefits 3.6 2.8 5.2 3.2 In addition, Kloos has decided to undertake exactly two of the projects. If plant expansion is selected, it will also modernize its current facilities. Formulate this problem as a binary programming problem in order to maximize projected benefits (in millions of dollars). (Let x; = 1 if project i is selected; 0 otherwise.) Max s.t. year 1 available capital year 2 available capital year 3 available capital exactly two projects constraint on plant expansion and modernization x₁ = 0, 1 Solve this problem. (X₁, X₂, X3, X₁) =

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