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
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
