Exam 8: Nonlinear Optimization Models

The key idea behind constructing an index fund is to choose a portfolio of securities that

Investment manager Max Gaines wishes to develop a mutual fund portfolio based on the Markowitz portfolio model. He needs to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the variance of the portfolio is minimized subject to the constraint that the expected return of the portfolio be at least 4%. Formulate the appropriate nonlinear program. ​ ​

The function f (X, Y) = X ² + Y ² has a single global minimum and is relatively easy to minimize.

​Discuss the essence of the pooling problem in terms of the circumstances, objective, and constraint

In the Bass model for forecasting the adoption of a new product, the objective function

The interpretation of the dual price for nonlinear models is different than the interpretation of the dual price for linear models.

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

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

Investment manager Max Gaines has several clients who wish to own a mutual fund portfolio that matches, as a whole, the performance of the S&P 500 stock index. His task is to determine what proportion of the portfolio should be invested in each of the five mutual funds listed below so that the portfolio most closely mimics the performance of the S&P 500 index. Formulate the appropriate nonlinear program. ​ ​

Components that share a storage facility are called

Components are referred to as pooled if they

Cutting Edge Yard Care is a residential and commercial lawn service company that has been in business in the Atlanta metropolitan area for almost one year. Cutting Edge would like to use its Atlanta service subscription data below to develop a model for forecasting service subscriptions in other metropolitan areas where it might expand. The first step is to estimate values for p (coefficient of innovation) and q (coefficient of imitation). Formulate the appropriate nonlinear program.

The measure of risk most often associated with the Markowitz portfolio model is the

Each point on the efficient frontier is the maximum possible risk, measured by portfolio variance, for the given return.

Which of the following is not a parameter of the Bass model for forecasting adoption of a new product?

If the coefficient of each squared term in a quadratic function is positive, the function is

Nonlinear optimization problems can have only one local optimal solution.

The value of the coefficient of imitation, q, in the Bass model for forecasting adoption of a new product cannot be negative.

​Provide several examples of both nonlinear objective functions and nonlinear constraints.

Pacific-Gulf Oil Company is faced with the problem of refining three petroleum components into regular and premium gasoline in order to maximize profit. Components 1 and 2 are pooled in a single storage tank and component 3 has its own storage tank. Regular and premium gasolines are made from blending the pooled components and component 3. Prices per gallon for the two products and three components, as well as product specifications, are listed below. ​ ​ The maximum number of gallons available for each of the three components is 4000, 8000, and 8000, respectively. Formulate a nonlinear program to determine: 1) what percentages of component 1 and component 2 should be used in the pooled mixture, and 2) how to make regular and premium gasoline by blending the mixture of components 1 and 2 from the pooling tank with component 3.