Chapter 10 Optimization in Profit Analysis

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Questions and Answers

What is a key difference between linear and nonlinear programming?

Linear programming is used for single-variable problems, while nonlinear programming is used for multi-variable problems.

Linear programming always has a guaranteed procedure to find a solution, whereas nonlinear programming does not. (correct)

Nonlinear programming is used for maximizing profit, while linear programming is used for minimizing cost.

Linear programming is used for profit analysis, while nonlinear programming is used for cost analysis.

What is the purpose of taking the derivative of the profit function in the profit analysis model?

To determine the feasibility of the solution space

To find the minimum profit

To graph the nonlinear profit curve

To find the maximum profit (correct)

What is the effect of adding the constraint 'price ≤ $20' to the profit analysis model?

It creates a feasible solution space (correct)

It reduces the feasible solution space

It has no effect on the feasible solution space

It increases the feasible solution space

What is a characteristic of the solution in nonlinear programming?

The solution may or may not be on the boundary of the feasible solution space Signup and view all the answers

What is the term used to describe the use of calculus to find optimal values for variables?

Classical optimization Signup and view all the answers

What is the type of model that consists of a single nonlinear objective function and no constraints?

Unconstrained optimization model Signup and view all the answers

What is the result of adding one or more constraints to an unconstrained optimization model?

A constrained optimization model Signup and view all the answers

What is the general form of a mathematical programming model?

An objective function subject to one or more constraints Signup and view all the answers

What is the main difference between linear programming and nonlinear programming?

The complexity of the solution Signup and view all the answers

What is the name of the model that was developed as an extension of the breakeven model?

Profit analysis model Signup and view all the answers

What is the term used to describe a model that has an objective function and/or constraints that are nonlinear?

Nonlinear programming model Signup and view all the answers

What is the reason why nonlinear programming problems are more complex to solve than linear programming problems?

The nonlinearity of the objective function and/or constraints Signup and view all the answers

What is the minimum expected annual return that Jessica Todd wants to achieve from her investment portfolio?

0.11 Signup and view all the answers

What is the purpose of the constraint that specifies all the money is invested?

To ensure all the money is invested Signup and view all the answers

What is represented by the decision variables xi in the nonlinear programming model?

The proportion of each stock in the portfolio Signup and view all the answers

Why are the covariance terms in the portfolio variance formula doubled?

To reflect all the different investment pairs in the matrix Signup and view all the answers

What is the objective of the nonlinear programming model?

To minimize the portfolio variance Signup and view all the answers

What is the purpose of the Lagrange multiplier in a nonlinear programming problem?

To reflect the approximate change in the objective function Signup and view all the answers

How do you access the sensitivity report in Excel Solver?

By clicking on 'Solve' and then 'Reports' Signup and view all the answers

What does the value of the Lagrange multiplier represent in the context of the labor constraint?

The change in the objective function per unit change in labor hours Signup and view all the answers

What is the purpose of the Solver Results screen in Excel?

To display the problem solution Signup and view all the answers

What is the relationship between the Lagrange multiplier and the dual value in a linear programming problem?

The Lagrange multiplier is analogous to the dual value Signup and view all the answers

What is the purpose of the Excel spreadsheet set up in Exhibit 10.9?

To solve the nonlinear programming model Signup and view all the answers

What is the relationship between the demand variables x1 and x2 in the Western Clothing Company example?

x1 and x2 are dependent variables Signup and view all the answers

Study Notes

Unconstrained Optimization

Unconstrained optimization models consist of a single nonlinear objective function and no constraints.
The solution to an unconstrained optimization model can be found by taking the derivative of the objective function, setting it equal to zero, and solving for the optimal value.

Constrained Optimization

Constrained optimization models consist of an objective function and one or more constraints.
Constrained optimization models are also known as nonlinear programming models.
The general form of a constrained optimization model is an objective function subject to one or more constraints.
The solution to a constrained optimization model is found by taking the derivative of the objective function, setting it equal to zero, and solving for the optimal value, while also considering the constraints.

Nonlinear Programming

Nonlinear programming models have an objective function and/or constraints that are nonlinear.
Nonlinear programming models are more complex than linear programming models and do not have a guaranteed procedure for finding a solution.
Nonlinear programming models can be solved using Excel's Solver feature.

Lagrange Multiplier

The Lagrange multiplier provides the dual value of a constraint in a nonlinear programming model.
The Lagrange multiplier represents the approximate change in the objective function resulting from a unit change in the quantity (right-hand-side) value of the constraint equation.

Nonlinear Programming Model with Multiple Constraints

A nonlinear programming model with multiple constraints can be formulated and solved using Excel.
The Western Clothing Company example illustrates a nonlinear programming model with multiple constraints, including resource constraints for denim cloth, cutting time, and sewing time.

Nonlinear Model Examples

Nonlinear models can be used in various fields, such as finance, to solve optimization problems.
The investor's problem of minimizing portfolio variance while achieving a minimum expected return can be formulated as a nonlinear programming model.
Nonlinear programming models can be solved using Excel's Solver feature.

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Description

This quiz covers the application of classical optimization to find optimal values for variables in profit analysis models. It expands on the breakeven model to develop a profit analysis model and involves substituting the demand function into the profit function.