Linear Programming Using Excel

Linear Programming Model

A mathematical approach to optimize a linear function subject to constraints defined by linear inequalities or equations.

Objective Function

A linear mathematical relationship that describes the firm's goal in terms of decision variables, such as maximizing profit or minimizing cost.

Decision Variables

Mathematical symbols that represent levels of activity in a firm, e.g., X1 = number of radios, X2 = number of toasters.

Constraints

Linear relationships that represent restrictions in the operational environment, modeled as inequalities or equalities.

Sensitivity Analysis

An analysis that examines how changes in the model coefficients affect the optimal solution.

Shadow Price

The change in the objective function value resulting from a one-unit increase in a constraint's right-hand side.

Non-negativity Constraints

Constraints that require decision variables to be greater than or equal to zero.

Objective Function Example

Max z = 40x1 + 50x2 is an example of an objective function for maximizing profit.

Constraint Example

1x1 + 2x2 <= 40 hr is an example of a constraint representing labor availability.

Applications of Linear Programming

Common applications include optimization in manufacturing, transportation, marketing, and agriculture.

Decision Variable Examples

C represents the number of ounces of compost and S represents sewage in a different linear programming model.

Minimization Objective Function

Min x = 6c + 3s is an example of an objective function for minimizing costs in a specific context.