Xpress Technologies offers complete web design, programming, implementation, and hosting services for customers. Xpress prices their services by the project and categorizes each customer request into one of three possible project categories: simple HTML design, requires Java/Flash coding, requires secure transaction capabilities. Xpress charges $3000 for each simple HTML design project, $5000 for each Java/Flash coding project, and $8000 for each project requiring secure transaction capabilities. Xpress has two types of employees that it assigns to these projects: graphic designers who make $32/hour and programmers who make $36/hour. The company currently has two graphic designers and four programmers; each employee can work up to a total of 40 hours per week. Xpress estimates that a simple HTML project will require 2 hours from the graphic designers and 4 hours from the programmers; projects requiring Java/Flash coding require 5 hours from the graphic designers and 6 hours from the programmers; projects requiring secure transaction capabilities require 7 hours from the graphic designers and 12 hours from the programmers. Xpress currently has requests for eight simple HTML projects, six Java/ Flash projects, and seven projects requiring secure transaction capabilities.
a. Develop a linear program that will help Xpress Technologies to choose which of the projects to accept for the coming week to maximize profits.
b. Find the optimal solution?