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Linear Programming — Multiple Plant Models
The following problem is based on a problem in section 4 of the book “Model Building in Mathematical Programming”. I’ve modified some aspects of it but it’s similar in nature. In my previous post I went over a basic method for solving linear programming problems with the example of a water plant that made two products.
Problem Description
In this post I will talk about using the same idea for linear programming problems with multiple subproblems. In this case we’ll be looking at a company which has two factories, factory A and factory B. The company makes bearings and produces two products which we’ll call grade I and grade II. Each of these produces a different profit, grade I makes $10 and grade II makes $12. The company gets a certain amount of raw material every week (here we’ll say 100 lbs) and splits it between the plants.
Factory A will get 60 units and factory B gets 40 units. Now it takes 4 lbs to produce each bearing. They grind the bearings and then polish them. Factory A has a grinding capacity of 80 hours per week and has a polishing capacity of 60 hours per week. Now it takes factory A four hours to grind the grade I bearings and two hours of labor to polish them. In contrast it takes them only two hours to grind the grade II bearings but five hours to polish them. From here we can write out what the linear program for factory A would look like.
Here we’re letting x1 be the number of units of grade I and x2 be the number of units of…