Exam 8: Nonlinear Optimization 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 cannot 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 − 3PL 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.

A function is considered a quadratic function if its nonlinear terms have a power of 2.​

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.

It is possible that a nonlinear application in which there is a single local optimal solution also shows that solution as the global optimal solution.

The minimum value for a convex function is 0,and the point (0,0)gives the minimum value of 0.