A manufacturer produces tables and chairs. Each product must go through 3 stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 4 hours assembly, 3 hours finishing, and 1 hour inspection. Each chair requires 3 hours assembly, 2 hours finishing, and 2 hours inspection. Selling price of table is P140 and chair is P90. Currently, each week, there are 220 hours assembly time available, 160 hours finishing time and 45 hours of inspection time. Assume that 1 hour of assembly time costs P5, 1 hour of finishing time costs P6, and 1 hour of inspection time costs P4.50. Whatever labor hours are not required for the tables and chairs can be applied to another product.

Questions:

1. Which describes a production problem, what would the objective function be?

2. Suppose it was decided that the labor hour costs have to be covered through the sale of the tables and chairs, regardless of whether or not all the labor hours are actually used. How would the objective function be written?

3. What if you realize that you can trade off assembly hours for finishing hours, but the total number of finishing hours, including the trade-off hours, cannot exceed 240 hours? How would this constraint be written?

4. What if the problem is modified to specify that 1/3 of the tables produced must have 6 chairs, 1/3 must have 4 chairs, and 1/3 must have 2 chairs. How will this constraint be written?