An electronics manufacturing company is planning a research and development program to handle a planned sequence of eight projects. The total budget available for the projects is $350,000. In addition, the company plans to hire 30 engineers for the entire program. If project 2 is selected, then project 7 should also be selected (but not vice versa). The anticipated profits and the resources needed for each project are shown in Table 1. Formulate a programming problem to determine the individual projects that the company should select in order to maximize its total profit.

Project Project Estimated Profit Project Expense Engineers Required 1 $290,000 $53,000 6 2 2 $510,000 $47,000 7 3 $340,000 $28,000 4 4 $160,000 $17,000 4 5 $560,000 $56,000 8 6 $410,000 $22,000 5 7 $340,000 $37,000 4 8 $560,000 $42,000 6 Table 1: Details for Each Potential Project in Scenario One