Problem:
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1.5 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $150 while the profit per chair is $90. Currently, each week there are 540 hours of assembly time available, 400 hours of finishing time, and 120 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:
Required:
Question: Formulate the linear program and determine the number of tables and chairs to produce to maximize profit.
Note: Explain the solution in detail.