A corporation has $60 million available for the coming year to allocate to its three subsidiaries. Because of commitments to stability of personnel employment and for other reasons, the corporation has established a range of funding for each subsidiary to be between a minimum of $10 million and a maximum of $30 million.

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. 

Define the decision variables and write the objective function and the constraints.

 

SUBSIDIARY 1 2 3 PROJECT 123 2 3 45 6 7 8 RATE OF RETURN 5% 9% 10% 7% 8% 8% 10% 6% UPPER LIMIT OF INVESTMENT $9 million $16 million $8 million No upper limit $10 million $10 million $13 million $7 million