A corporation has $60 million available for the coming year to allocate to its three subsidiaries. Because
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Question:
To maintain some degree of equity among Subsidiary 2 and 3, the corporation wants Subsidiary 3 to receive no more than twice the funding for Subsidiary 2. Owing to the nature of its operation, Subsidiary 1 cannot utilize more than $20 million without major new capital expansion. The corporation is unwilling to undertake such expansion currently.
The funding for each subsidiary will be used to fund several projects it undertakes (see table below). A rate of return (as a percent of investment) has been established for each project. In addition, certain of the projects permit only limited investment. The data of each project is given below. For example, the maximum subsidiary 1 can invest in project 2 is $16 million and for every $100 invested in project 2 the company earns $9 profit (return on investment).
Formulate a linear programming problem that maximizes the total return (in $million) on all investments for the corporation. Of course, the corporation wants to know how to allocate its investment budget to the three subsidiaries and their projects.
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