Lecture #8 - Linear Programming

Assumptions

1.​ Limited resources
2.​ Explicit objectives
3.​ Linearity
4.​ Homogeneity
5.​ Divisibility



Parts of a Linear Program

●​ Objective (target cells)
●​ Decision cells (changing cells)
●​ Constraints



Maximization Problems




Minimization Problems

, Building a Linear Program

1.​ Identify and describe the objective
2.​ Identify and describe the decision variables
3.​ Identify and describe each constraints
4.​ Add non-negativity constraints
5.​ Combine everything into the model



Fuel & Solvent Company

You work at a company that produces two products: a fuel additive and a solvent. Each
of these products is formed from a combination of three materials.

OPTIMIZATION PROBLEM
You have been asked to find the best combination of products that will maximize
potential profit.



Objective

●​ Each ton of fuel yields a profit of $40
●​ Each ton of solvent yields a profit of $30

→ Maximum profit = $40 x Fuel + $30 x Solvent


Decision Cells

You have been asked to find the best combination of products that will maximize
potential profit.

DECISION CELLS
●​ Quantity (tons) of fuel
●​ Quantity (tons) of solvent