Exam 12: Advanced Optimization Application

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

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

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

MegaSports,Inc.produces two high-priced metal baseball bats,the Slugger and the Launcher,that are made from special aluminum and steel alloys.The cost to produce a Slugger bat is $100,and the cost to produce a Launcher bat is $120.We can not assume that MegaSports will sell all the bats it can produce.As the selling price of each bat model - Slugger and Launcher - increases,the quantity demanded for each model goes down. Assume that the demand,S,for Slugger bats is given by S = 640 - 4P_S and the demand,L,for Launcher bats is given by L = 450 - 3P_L where P_S is the price of a Slugger bat and P_L is the price of a Launcher bat.The profit contributions are P_S S - 100S for Slugger bats and P_L L - 120L for Launcher bats.Develop the total profit contribution function for this problem.

In the case of functions with multiple local optima,most nonlinear optimization software methods can get stuck and terminate at a local optimum.

Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk.His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides an annual return of no less than 3%.Formulate the appropriate linear program.

Nonlinear programming algorithms are more complex than linear programming algorithms.

Native Customs sells two popular styles of hand-sewn footwear: a sandal and a moccasin.The cost to make a pair of sandals is $18,and the cost to make a pair of moccasins is $24.The demand for these two items is sensitive to the price,and historical data indicate that the monthly demands are given by S = 400 - 10P₁ and M = 450 - 15P₂ , where S = demand for sandals (in pairs),M = demand for moccasins (in pairs),P₁ = price for a pair of sandals,and P₂ = price for a pair of moccasins.To remain competitive,Native Customs must limit the price (per pair)to no more than $60 and $75 for its sandals and moccasins,respectively.Formulate this nonlinear programming problem to find the optimal production quantities and prices for sandals and moccasins that maximize total monthly profit.

For a typical nonlinear problem,duals price are relatively insensitive to small changes in right-hand side values.

Revenue management methodology enables an airline to maximize the number of full-fare seats it sells on each flight.

Revenue management methodology can be applied in the case of nonperishable assets.

Portfolio manager Max Gaines needs to develop an investment portfolio for his conservative clients.His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides the best return possible with a minimum risk.Formulate the maximin linear program.

Revenue management methodology was originally developed for the banking industry.

The Markowitz mean-variance portfolio model is a classic application of non-linear programming.

The overall goal of portfolio models is to create a portfolio that provides the best balance between

A convex function is

There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.

The objective for the Markowitz portfolio model is to minimize portfolio return variance.

A function is quadratic if its nonlinear terms have a power of 4.

A key trade-off in most portfolio optimization models must be made between risk and return.