A corporation has two divisions (the Eastern Division and the Western Division) that operate semiautonomously, with each developing and marketing its own products. However, to coordinate their product lines and to promote efficiency, the divisions compete at the corporate level for investment funds for new product development projects. In particular, each division submits its proposals to corporate headquarters in September for new major projects to be undertaken the following year, and available funds are then allocated in such a way as to maximize the estimated total net discounted profits that will eventually result from the projects.
For the upcoming year, each division is proposing three new major projects. Each project can be undertaken at any level, where the estimated net discounted profit would be proportional to the level. The relevant data on the projects are summarized as follows:
A total of $150,000,000 is budgeted for investment in these projects.

(a) Formulate this problem as a multidivisional linear programming problem.
(b) Construct the corresponding table of constraint coefficients having the block angular structure shown in Table 23.4.

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Eastern Division Project Western Division Project 1 2 3 Level Required investment (in millions of dollars) Net profitability Facility restriction Labor restriction XX2 16X1 7x2 13x 7x1 3x2 5x3 10x 3x2 7x3 50 4x, 2x2 + 5x 30 8x4 20xs 10x 4x 7xs 5x 6x4 + 13x5 9x6 s: 45 3x4 8xs+2x6 25