How to create a linear programming model for this

[SillyJane]

I have been studying Algebraic functions and also how to solve problems using 'matrices' and 'Linear Programming'. With that in mind i am suppose to imagine i am the manager of a company that manufactures two to three types of products. I must develop a linear program with a solution that gives how many of each type of product the company should produce. Then perform an analysis on various aspects of the model. I have to assume reporting to a boss, and must convince the boss that my analysis is correct. I must present my findings in a way that will convince him/her not only of my analysis, but also of my ability and worth to the company. Must be creative and innovative using those mathematical principles. What do i do here? i am so confused....

Thanks

 

[JeffM]

I have been studying Algebraic functions and also how to solve problems using 'matrices' and 'Linear Programming'. With that in mind i am suppose to imagine i am the manager of a company that manufactures two to three types of products. I must develop a linear program with a solution that gives how many of each type of product the company should produce. Then perform an analysis on various aspects of the model. I have to assume reporting to a boss, and must convince the boss that my analysis is correct. I must present my findings in a way that will convince him/her not only of my analysis, but also of my ability and worth to the company. Must be creative and innovative using those mathematical principles. What do i do here? i am so confused....

Thanks

What is linear programming? It is a method to optimize a linear objective function subject to linear constraints.

So you are to construct a problem that has a linear objective function and linear constraints. Furthermore the exercise requires the problem to involve production of two or three different types of product. Different products usually have different costs, different market prices, and different levels of sales, which may or may not be interdependent. Different products may require the use of the same production facilities, and so production may be interdependent. Look at some of the problems in your book. You are just being asked to make up your own problem and then to solve it.

What do businesses usually want to optimize? Normally, they want to maximize profits. So that suggests the objective function should be a function that represents profit. Now imagine a set of linear constraints that may affect profit. These might involve pricing, sales, trade-offs among production. Use your imagination to think of the most complex problem that you can solve and write up in the time assigned.