Question
I am working on basic linear programming for a forest management class and am having trouble setting up the problem. I'm not quite sure what
I am working on basic linear programming for a forest management class and am having trouble setting up the problem. I'm not quite sure what the decision values are. I know the constraints and that they're looking to meet the EPA pollution limit while still supporting the mill, but I'm confused to the decision variables and objective function. Could you please help me recognize the decision variables and discuss what values would go into the objective function with it? Could you also explain how the employee value fits into the problem? The problem is below. Thank you.
"A pulp mill makes mechanical and chemical pulp. Unfortunately, it also pollutes the river into which it discharges its waste water. The EPA has ordered the mill to reduce its pollution, which is measured by the biological oxygen demand (BOD) of the effluent. The original owners decided that the mill would lose too much money if it reduced its pollution levels to meet the EPA's expectations. The mill has been purchased from the original owners by the employees and local businesses, who now own and operate the mill as a cooperative.
The new mill managers have developed the following objectives for operating the mill: - Limit pollution to no more than 350 BOD units per day (EPA requirement). - Generate at least $40,000 of net revenue per day (needed for payments on the mill). - Within these limits, maximize employment.
Use the following data to formulate this problem as linear program: - Both chemical and mechanical pulp require the labor of one worker for about 1 day, or 1 workday (wd), per ton produced. - Net revenue per ton of chemical pulp is $200/ton, $100/ton for mechanical pulp. - One BOD unit is discharged per ton of mechanical pulp produced, and 1.5 BOD units are discharged per ton of chemical pulp produced. - The maximum capacity of the mill to make mechanical pulp is 300 tons per day; for chemical pulp, it is 200 tons per day. The two manufacturing processes are independent; that is, the mechanical pulp line cannot be used for making chemical pulp or vice versa."
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started