Exam 16: Nonlinear and Non-Smooth Optimization

Use the table below to answer the following question(s). Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates)of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. Bungalow Location Data X-coordinate Y -coordinate Trips/Month Location 0 0 6 Bungalow 1 25 100 30 Bungalow 2 20 75 15 Bungalow 3 90 80 28 Bungalow 4 60 100 10 -Which of the following is the ideal next step if you get the message "Solver has converged to the current solution./All constraints are satisfied," when using Solver for nonlinear optimization models?

Use the table below to answer the following question(s). Jonathan Reese is considering three stocks in which to invest with a fixed budget.The table below provides information on Jonathan's expected returns for each stock.The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks.He expects a total return of at least 10%. Develop a quadratic optimization model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix. -According to the model, what is the squared term value for Stock 1 variance?

Use the table below to create a nonlinear model based on the table to answer the following question(s). The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues.They have three classes of tickets: Classic, Silver, and Gold.The table below provides information on the average ticket sales, revenue and price elasticity on demand.They have a total seating capacity of 300.The table also provides the price range within which they plan to reduce their ticket rates. -Which of the following is the rectilinear distance between the points A(13,15)and B(10,12)?

Jonathan Reese is considering three stocks in which to invest with a fixed budget.The table below provides information on Jonathan's expected returns for each stock.The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks.He expects a total return of at least 10%. Using the table above, provide the objective function for minimal variance, and the constraints for creating an optimization model.

Use the table below to answer the following question(s). Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates)of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. Bungalow Location Data X-coordinate Y -coordinate Trips/Month Location 0 0 6 Bungalow 1 25 100 30 Bungalow 2 20 75 15 Bungalow 3 90 80 28 Bungalow 4 60 100 10 -According to the model, what is the distance between Shirley's new accommodation and Bungalow 4?

List the four major categories of inventory costs and explain how they are influenced by the timing of the ordering decision and amount ordered.

According to the model, which of the following production cells covers the most distance according to its demand when using the phone charger?

According to the model, which of the following is the Y-coordinate for the phone charger location?

For nonlinear models, the Lagrange multipliers are only approximate indicators of shadow prices.

Use the table below to answer the following question(s). Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates)of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. Bungalow Location Data X-coordinate Y -coordinate Trips/Month Location 0 0 6 Bungalow 1 25 100 30 Bungalow 2 20 75 15 Bungalow 3 90 80 28 Bungalow 4 60 100 10 -According to the model, which of the following bungalows is Shirley's new accommodation closest to?

Use the table below to answer the following question(s). Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates)of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. Bungalow Location Data X-coordinate Y -coordinate Trips/Month Location 0 0 6 Bungalow 1 25 100 30 Bungalow 2 20 75 15 Bungalow 3 90 80 28 Bungalow 4 60 100 10 -According to the model, what is the distance between Shirley's new accommodation and Bungalow 1?

Use the table below to answer the following question(s). Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates)of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. Bungalow Location Data X-coordinate Y -coordinate Trips/Month Location 0 0 6 Bungalow 1 25 100 30 Bungalow 2 20 75 15 Bungalow 3 90 80 28 Bungalow 4 60 100 10 -According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 2?

A global optimum solution is one for which all points close by are no better than the solution.

Absolute value functions, in optimization models, result in non-smooth functions.

Use the table below to answer the following question(s). Jonathan Reese is considering three stocks in which to invest with a fixed budget.The table below provides information on Jonathan's expected returns for each stock.The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks.He expects a total return of at least 10%. Develop a quadratic optimization model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix. -According to the model, what is the expected variance of the resulting portfolio?

Use the table below to answer the following question(s). -Bolton Computers are planning to release a new line of low-end laptops.Using Excel's Solver, develop a nonlinear model to calculate the optimal price for the laptops, given that sales = -3.85 × price + 1150.9.

Use the table below to answer the following question(s). Jonathan Reese is considering three stocks in which to invest with a fixed budget.The table below provides information on Jonathan's expected returns for each stock.The table also provides information, collected from market researchers, on the variance-covariance matrix of the individual stocks.He expects a total return of at least 10%. Develop a quadratic optimization model to find the optimal allocation of the budget to each stock, and variance calculations for squared terms and cross-products based on the variance-covariance matrix. -According to the model, what is the cross-product value for Stock 1 variance?

Use the table below to answer the following question(s). Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates)of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. Bungalow Location Data X-coordinate Y -coordinate Trips/Month Location 0 0 6 Bungalow 1 25 100 30 Bungalow 2 20 75 15 Bungalow 3 90 80 28 Bungalow 4 60 100 10 -According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 5?

Pickson Luthiers Corporation is studying where to locate a phone charging point on the factory floor.The locations of five production cells are expressed as X- and Y-coordinates on a rectangular grid of the factory layout.The daily demand for the charging point (measured as the number of trips to the charging point)at each production cell is also known.Because of the nature of the equipment layout in the factory and for safety reasons, workers must travel along marked horizontal and vertical aisles to access the charger.Thus, the distance from a cell to the charger is measured as rectilinear distance. The table below provides the relevant information. The optimal location should minimize the total weighted distance between the charging point and all production cells, where the weights are the daily number of trips to the phone charging point. From the above table, provide the objective function for the best location of the charging point.What kind of solution technique from Solver can be used to make the optimization model based on the data?

Use the table below to answer the following question(s). Shirley Templeton is a real estate agent for Paralol Realty.Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows.These 5 bungalows are situated in close proximity.In order to make traveling easire, Shirley decides to move to a location closer to the 5 bungalows.The table below gives the location (X and Y coordinates)of the 5 bungalows along with the number of trips she would have to make to each bungalow.Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. Bungalow Location Data X-coordinate Y -coordinate Trips/Month Location 0 0 6 Bungalow 1 25 100 30 Bungalow 2 20 75 15 Bungalow 3 90 80 28 Bungalow 4 60 100 10 -According to the model, what is the distance between Shirley's new accommodation and Bungalow 2?