Paulette Smith and Maureen Becker are seniors in engineering and business, respectively, at State University. They have set up a company, PM Computer Services, to assemble and sell their own brand of personal computers. They buy component parts on the open market from a variety of sources in the United States and overseas, and they assemble their computers, mostly at night, in their three-bedroom apartment. They sell their computers primarily to departments at State University and to other students. They hire other students to perform the assembly operations and to test and package the computers. In addition to managing the operations, Paulette and Maureen help with all other tasks, including sales and accounting.

They pay the students who work for them $8 per hour for a 40-hour week, or $1,280 per month. They hire students on a monthly basis, and their delivery schedule is also on a monthly (i.e., end-of-the-month) basis. PM currently has five employees. PM Computers has determined that each of its employees is able to produce 12.7 computers, on average, per month. When the monthly demand for its computers exceeds its regular production capacity, PM employs limited overtime. Each computer produced on an overtime basis adds $12 to the labor cost of a computer. A PM employee can produce 0.6 computer per month on an overtime basis.

Paulette and Maureen have received the following computer orders for the next 6 months:

Month i Computer Orders

1 63

2 74

3 95

4 57

5 68

6 86

In the past, PM has met its demand strictly from regular and overtime production. To meet demand in some months when it did not have sufficient regular and overtime production, the company would plan ahead and produce computers in previous months with available capacity. However, Paulette and Maureen's apartment was completely filled with components and workspace, so they could not store completed computers. Instead, they leased warehouse space in town to store their completed computers for delivery in future months. They had to transport the computers across town to the warehouse and pay for all handling; also, the warehouse had to be climate controlled. The cost of holding a computer in storage at the warehouse is $15 per month.

Paulette and Maureen are considering an alternative production strategy wherein they would hire new workers on a monthly basis as needed and lay off workers when they are not needed. They estimate the cost of hiring new workers to be $200, primarily for related paperwork and training. The cost of laying off a worker is $320, or approximately 1 week's wages. They may want to rehire some of the workers they lay off at a later date, so they want them to leave with a good feeling about PM.

Determine a planning schedule for PM Computer Services, indicating the number of employees working each month, including the number hired and the number laid off, the number of computers produced each month in both regular time and overtime, and the number of computers carried over in inventory each month. There should be no inventory left over after month 6. Provide integer solution values for these different variables. Compare this solution with the one you would obtain without integer restrictions.