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 -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?

What is the importance of Integer Tolerance in Solver?

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 2?

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.). -Which of the following best defines a binary variable?

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.). -What is the minimum number of total part-time employees needed across all the 4-hour shifts to ensure meeting the staffing requirements?

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 cash used for Project 2?

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 total weighted distance that Shirley would travel between the bungalows?

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 1 variance?

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 total projected revenue for the new sales figures?

What is a job-sequencing problem? How can we find an optimal solution for such problems?

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 3 variance?

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 Silver tickets at the new price?

If the Integer Tolerance is set to 0.01, the Solver will stop if it finds an integer solution that is within 10% of the optimal solution.