This is a variation on the preceding exercise. The head of the programming support group realizes that not all of the programmers in the group can work on each of the fourteen proposed projects. Specifically, three types of programming are required for the projects: Excel programming, Access programming, and C programming. Not all of the programmers know each of these types of programming.

The following table shows the number of hours of each type of programming required for each project. There is a total of 9000 potential hours of Excel programming available, a total of 7200 potential hours of Access programming available, and a total of 3600 potential hours of C programming available. In addition, 9100 hours of total programming time are available to distribute across the three types of programming. Assume that the total benefit for a portfolio of projects is equal to the sum of the values for each project in the portfolio.

Determine the portfolio of projects that provides the largest benefit subject to the constraints on the amount of programming time of each type that is available in addition to the constraint on the total number of hours of programming time that is available