Exam 12: Advanced Optimization Application

Skooter's Skateboards produces two models of skateboards,the FX and the ZX.Skateboard revenue (in $l,000s)for the firm is nonlinear and is stated as (number of FXs)(5 - 0.2 number of FXs)+ (number of ZXs)(7 - 0.3 number of ZXs).Skooter's has 80 labor-hours available per week in its paint shop.Each FX requires 2 labor-hours to paint and each ZX requires 3 labor-hours.Formulate this nonlinear production planning problem to determine how many FX and ZX skateboards should be produced per week at Scooter's.

A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.

Revenue management methodology enables an airline to

A feasible solution is a global optimum if there are no other feasible points with a better objective function value in the feasible region.

Modern revenue management systems maximize revenue potential for an organization by helping to manage

Many linear programming algorithms such as the simplex method optimize by examining only the extreme points of the feasible region.

Each point on the efficient frontier graph associated with the Markowitz portfolio model is the

Functions that are convex have a single local maximum that is also the global maximum.

Which of the following is incorrect?

LeapFrog Airways provides passenger service for Indianapolis,Baltimore,Memphis,Austin,and Tampa.LeapFrog has two WB828 airplanes,one based in Indianapolis and the other in Baltimore.Each morning the Indianapolis based plane flies to Austin with a stopover in Memphis,and the Baltimore based plane flies to Tampa with a stopover in Memphis.Both planes have a coach section with a 120-seat capacity. LeapFrog uses two fare classes: a discount fare D class and a full fare F class.Leapfrog's products,each referred to as an origin destination itinerary fare (ODIF),are listed below with their fares and forecasted demand. Develop a linear programming model for LeapFrog's problem situation and determine how many seats LeapFrog should allocate to each ODIF.

An index fund is an example of passive asset management.

To develop a portfolio that provides the best return possible with a minimum risk,the linear programming model will have an objective function which

Because most nonlinear optimization codes will terminate with a local optimum,the solution returned by the codes will be the best solution.

Hervis Car Rental in Austin,TX has 50 high-performance Shelby-H Mustangs in its rental fleet.These cars will be in greater demand than usual during the last weekend in July when the Central Texas Mustang Club holds its annual rally in Austin.At times like this,Hervis uses a revenue management system to determine the optimal number of reservations to have available for the Shelby-H cars. Hervis has agreed to have at least 60% of its Shelby-H Mustangs available for rally attendees at a special rate.Although many of the rally attendees will request a Saturday and Sunday two-day package,some attendees may select a Saturday only or a Sunday only reservation.Customers not attending the rally may also request a Saturday and Sunday two-day package,or make a Saturday only or Sunday only reservation.Thus,six types of reservations are possible.The cost for each type of reservation is shown here. The anticipated demand for each type of reservation is as follows: Hervis Car Rental would like to determine how many Shelby-H Mustangs to make available for each type of reservation in order to maximize total revenue. a.Define the decision variables. b.Formulate a linear programming model for this revenue management application.

The goal of portfolio models is to create a portfolio that provides the best balance between risk and return.

Lymann Brothers has a substantial number of clients who wish to own a mutual fund portfolio that closely matches the performance of the S&P 500 stock index.A manager at Lymann Brothers has selected five mutual funds that will be considered for inclusion in the portfolio.The manager must decide what percentage of the portfolio should be invested in each mutual fund. Minimize the variance of the portfolio subject to constraints on the expected return,assuming that Lymann Brothers' client requires the expected portfolio return to be at least 9 percent.

Revenue management methodology was originally developed for

In portfolio models,risk is minimized by diversification.

For a minimization problem,a point is a global minimum if there are no other feasible points with a smaller objective function value.

A feasible solution is a global optimum if there are no other feasible solutions with a better objective function value in the immediate neighborhood.