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Lecture #8 - Linear Programming

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Identify the objective, decision cells, and constraints in an optimization problem. Set up an optimization problem in Excel. Set up Solver to solve an optimization problem in Excel.

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  • December 31, 2024
  • 4
  • 2024/2025
  • Class notes
  • Asim shrestha
  • Lecture #8 - linear programming
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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

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