A small computer manufacturing company produces both laptop and desktop computers. The production of a laptop computer requires 4 hours of assembly and 1 hour of testing time. The production of a desktop computer requires 4 hours of assembly and 1.5 hours of testing time. The profit margin for a laptop computer is $400, and the profit margin for a desktop computer is $500. There are a total of 5,000 hours of assembly time and 1,000 hours of testing time available every week. The company has decided to produce at least twice as many laptop computers as desktop computers.
a. Assuming unlimited demand for both laptop and desktop computers, formulate a linear programming problem.
b. Solve the problem using the graphical method.