Exam 14: Integer and Nonlinear Optimization Models

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. Pickson Luthiers Corporation Phone Recharging Points Data Cell X -coordinate Y -coordinate Demand Measurements 2 5 27 Paint 1 3 12 Electricals 4 2 25 Testing 3.5 5 5 Packaging 3 3 7 Maximum 4 5 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 questions). 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 easier, 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 Locatim X-coardinate Y-coardinate Trips/Month Bungaldw 1 0 0 6 Bungaldw 2 25 100 30 Bungaldw 3 20 75 15 Bungaldw 4 90 80 28 Bungaldw 5 60 100 10 -According to the model, what is the distance between Shirley's new accommodation and Bungalow 5?

Use the table below to answer the following questions). 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 easier, 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 Locatim X-coardinate Y-coardinate Trips/Month Bungaldw 1 0 0 6 Bungaldw 2 25 100 30 Bungaldw 3 20 75 15 Bungaldw 4 90 80 28 Bungaldw 5 60 100 10 -According to the model, what is the Y-coordinate for the location of Shirley's new accommodation?

Use the table below to answer the following questions). 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%. Reese's Stuck Investment Plan Data Expected Variance-Covariance Matrix Return Stack 1 Stack 2 Stack 3 Stack 1 10\% Stack 1 0.021 0.018 -0.003 Stack 2 11\% Stack 2 0.018 0.070 0.006 Stack 3 9\% Stack 3 -0.003 0.006 0.003 Target Retum 10\% Develop a Nonlinear Optimization Models 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 2 variance?

All Nonlinear Optimization Models models have nonlinear constraints.

Use the table below to answer the following questions). 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 easier, 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 Locatim X-coardinate Y-coardinate Trips/Month Bungaldw 1 0 0 6 Bungaldw 2 25 100 30 Bungaldw 3 20 75 15 Bungaldw 4 90 80 28 Bungaldw 5 60 100 10 -According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 4?

Use the table below to answer the following questions). 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 easier, 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 Locatim X-coardinate Y-coardinate Trips/Month Bungaldw 1 0 0 6 Bungaldw 2 25 100 30 Bungaldw 3 20 75 15 Bungaldw 4 90 80 28 Bungaldw 5 60 100 10 -According to the model, what is the distance between Shirley's new accommodation and Bungalow 3?

Use the table below to answer the following questions). 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 easier, 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 Locatim X-coardinate Y-coardinate Trips/Month Bungaldw 1 0 0 6 Bungaldw 2 25 100 30 Bungaldw 3 20 75 15 Bungaldw 4 90 80 28 Bungaldw 5 60 100 10 -According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 1?

Use the table below to answer the following questions). 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%. Reese's Stuck Investment Plan Data Expected Variance-Covariance Matrix Return Stack 1 Stack 2 Stack 3 Stack 1 10\% Stack 1 0.021 0.018 -0.003 Stack 2 11\% Stack 2 0.018 0.070 0.006 Stack 3 9\% Stack 3 -0.003 0.006 0.003 Target Retum 10\% Develop a Nonlinear Optimization Models 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?

The economic order quantity is the amount to order that minimizes the total cost of ordering and holding.

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions). 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. Pickson Luthiers Corporation Phone Recharging Points Data Cell X -coordinate Y -coordinate Demand Measurements 2 5 27 Paint 1 3 12 Electricals 4 2 25 Testing 3.5 5 5 Packnging 3 3 7 Maxirnum 4 5 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. Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.) -According to the model, which of the following is the weighted distance between the phone charger and Measurements cell?

LO1: Develop and solve nonlinear optimization models for different applications. Use the table below to answer the following questions). 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. Pickson Luthiers Corporation Phone Recharging Points Data Cell X -coordinate Y -coordinate Demand Measurements 2 5 27 Paint 1 3 12 Electricals 4 2 25 Testing 3.5 5 5 Packnging 3 3 7 Maxirnum 4 5 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. Create a nonsmooth optimization model, based on the data, to answer the following questions. Hint: Choose the closest answers.) -According to the model, which of the following production cells covers the most distance according to its demand when using the phone charger?

Use the table below to answer the following questions). 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 easier, 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 Locatim X-coardinate Y-coardinate Trips/Month Bungaldw 1 0 0 6 Bungaldw 2 25 100 30 Bungaldw 3 20 75 15 Bungaldw 4 90 80 28 Bungaldw 5 60 100 10 -According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 3?

Use the table below to answer the following questions). 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 easier, 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 Locatim X-coardinate Y-coardinate Trips/Month Bungaldw 1 0 0 6 Bungaldw 2 25 100 30 Bungaldw 3 20 75 15 Bungaldw 4 90 80 28 Bungaldw 5 60 100 10 -According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 5?

Use the table below to create a nonlinear model based on the table to answer the following questions). 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. Atlas Mavie Theater Ticketing Data Ticket Class Current Rate Avernge Daily Sald Elasticity Tatal Seating Capacity Price Range Classic \ 8.45 150 -1.5 300 \ 6.50 \ 7.50 Silver \ 13.25 -2 \ 1.50 \ 12.50 Gald \ 17.50 -1 \ 15.50 \ 16.50 -According to the nonlinear model, what is the new price for Gold tickets?

Use the table below to answer the following questions). 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%. Reese's Stuck Investment Plan Data Expected Variance-Covariance Matrix Return Stack 1 Stack 2 Stack 3 Stack 1 10\% Stack 1 0.021 0.018 -0.003 Stack 2 11\% Stack 2 0.018 0.070 0.006 Stack 3 9\% Stack 3 -0.003 0.006 0.003 Target Retum 10\% Develop a Nonlinear Optimization Models 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 percentage of the budget should be allocated to Stock 3?

Use the table below to answer the following questions). 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 easier, 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 Locatim X-coardinate Y-coardinate Trips/Month Bungaldw 1 0 0 6 Bungaldw 2 25 100 30 Bungaldw 3 20 75 15 Bungaldw 4 90 80 28 Bungaldw 5 60 100 10 -According to the model, what is the distance between Shirley's new accommodation and Bungalow 4?

Use the table below to answer the following questions). 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 easier, 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 Locatim X-coardinate Y-coardinate Trips/Month Bungaldw 1 0 0 6 Bungaldw 2 25 100 30 Bungaldw 3 20 75 15 Bungaldw 4 90 80 28 Bungaldw 5 60 100 10 -According to the model, what is the weighted distance between Shirley's new accommodation and Bungalow 2?

Use the table below to answer the following questions). 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%. Reese's Stuck Investment Plan Data Expected Variance-Covariance Matrix Return Stack 1 Stack 2 Stack 3 Stack 1 10\% Stack 1 0.021 0.018 -0.003 Stack 2 11\% Stack 2 0.018 0.070 0.006 Stack 3 9\% Stack 3 -0.003 0.006 0.003 Target Retum 10\% Develop a Nonlinear Optimization Models 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 percentage of the budget should be allocated to Stock 2?

What is the total return obtained from all five projects?