Exam 14: Integer and Nonlinear Optimization Models

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 X-coordinate for the location of Shirley's new accommodation?

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, which of the following is the projected sales figure for Classic tickets at the new price?

Use the table below to answer the following questions) using the standard Solver. A company makes standard 130-inch-wide rolls of thin sheet metal and slits them into smaller rolls to meet customer orders for widths of 10, 14, and 25 inches. Suppose that the company has proposed the following cutting patterns: A 1 Cutting-Stock Problem 2 3 Data 4 Pattein 10-in rolls 14 in. rolls 25-in. rolls Scrap 5 1 0 8 0 10 6 2 0 2 3 10 7 3 3 0 3 4 8 4 10 0 0 10 9 5 3 2 2 4 10 6 8 2 0 4 Demands for the coming week are 950 10-inch rolls, 725 14-inch roles, and 640 25-inch rolls. Develop a model using the Analytic Solver Platform that will determine how many 130-inch rolls to cut into each of the six patterns in order to meet demand and minimize scrap. -What is the total number of 10-inch rolls produced?

Use the table below to answer the following questions) using the standard Solver. Coppell Services contracts with outsourcing partners to handle various customer service functions. Based on a study of call volumes provided by one of the firm's partners, the minimum number of staff needed for each hour of the day is as follows: Hour Minimum Staff Required 8-9 6 9-10 10 10-11 12 11- noon 10 noon-1 8 1-2 16 2-3 15 3-4 20 4-5 15 Mr. Coppell hires 6 permanent employees and wants to staff the remaining requirements using part-time employees who work 4-hour shifts four consecutive hours starting as early as 8 A.M. or as late as 1 P.M.). -How many part-time employees are present in the 3-4 time slot?

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, which of the following is the projected revenue figure for Silver tickets based on its new price?

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 total return on all stocks?

Use the table below to answer the following questions) by invoking the binary constraints on the variables using the standard Solver. Below is the spreadsheet for a project selection model: A D E F G 1 Project Selection Model 2 3 Data 4 Available Project 1 Project 2 Project 3 Project 4 Project 5 Resources Expected Return \ 160,000 \ 200,000 \ 125,000 \ 150,000 \ 225,000 5 NPV) 6 Cash requirements \ 45,000 \ 70,000 \ 28,000 \ 52,000 \ 65,000 \ 175,000 7 Personnel requirements 7 4 2 6 4 10 8 9 Model 10 Project selection 11 decisions 12 Cash Used 13 Personnel Used 14 Return -What is the amount of personnel used for Project 2?

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 Silver 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 is the squared term value for Stock 1 variance?

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 Packaging 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 is the weighted distance between the phone charger and Paint cell?

Explain the travelling salesperson problem with examples.

What should be the value of Integer Tolerance in order to find the guaranteed optimal integer solution?

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, which of the following is the projected revenue figure for Classic tickets based on its new price?

Stone Age Surfboards is a small manufacturer of two types of popular low-tide surfboards, the Graystone and the Lava models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 8 skilled workers, each of whom works 9.25 hours per day. The finishing department has 5 workers, each of whom works a 6-hour shift per day. Each pair of Graystone surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the Graystone model and $60 on the Lava model. The company anticipates selling at least twice as many Lava models as Graystone models. Use the spreadsheet below for Stone Age Surfboards to answer the following questions) using integer constraints on variables in the optimization models using the standard Solver. -Which of the following constraints does Solver use?

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 squared term value for Stock 2 variance?

Use the table below to answer the following questions) using the standard Solver. Coppell Services contracts with outsourcing partners to handle various customer service functions. Based on a study of call volumes provided by one of the firm's partners, the minimum number of staff needed for each hour of the day is as follows: Hour Minimum Staff Required 8-9 6 9-10 10 10-11 12 11- noon 10 noon-1 8 1-2 16 2-3 15 3-4 20 4-5 15 Mr. Coppell hires 6 permanent employees and wants to staff the remaining requirements using part-time employees who work 4-hour shifts four consecutive hours starting as early as 8 A.M. or as late as 1 P.M.). -How many excess employees are present in the 4-5 time slot?

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 1?

Use the table below to answer the following questions) by invoking the binary constraints on the variables using the standard Solver. Below is the spreadsheet for a project selection model: A D E F G 1 Project Selection Model 2 3 Data 4 Available Project 1 Project 2 Project 3 Project 4 Project 5 Resources Expected Return \ 160,000 \ 200,000 \ 125,000 \ 150,000 \ 225,000 5 NPV) 6 Cash requirements \ 45,000 \ 70,000 \ 28,000 \ 52,000 \ 65,000 \ 175,000 7 Personnel requirements 7 4 2 6 4 10 8 9 Model 10 Project selection 11 decisions 12 Cash Used 13 Personnel Used 14 Return -Which of the following cells is set as the objective cell in Solver?

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 Y-coordinate for the phone charger location?