Exam 14: Integer and Nonlinear Optimization Models

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 scrap produced?

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. -What is the total number of hours used for the finishing operation?

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 Gold tickets based on its new price?

Rectilinear distance is the measure of distance as a straight line between two points.

Decision variables that are forced to be integers are called general integer variables.

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. -What is the quantity of Lava surfboards produced?

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 total amount of cash used for all five projects?

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. -What is the total number of hours used for fabrication?

Explain the method of Integer Linear Optimization Models.

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. -What is the quantity of Graystone surfboards produced?

Use the table below to answer the following questions). Bolton Computer's Laptop Pricing Decision Inputs Price model sales -3.85\timesprice+1150.9 outputs total revenue sales \times price -According to the nonlinear model, which of the following is the total revenue expected from the sales?

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 Electricals cell?

Use the table below to answer the following questions). Bolton Computer's Laptop Pricing Decision Inputs Price model sales -3.85\timesprice+1150.9 outputs total revenue sales \times price -According to the nonlinear model, which of the following is the expected sales figure based on the computed price?

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 8-9 time slot?

Explain how the Markowitz portfolio model is a Nonlinear Optimization Models model.

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 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, what is the new price for Classic tickets?

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 Stock Investment Plan Data Expected Variance-Covariance Matrix Return Stock 1 Stock 2 Stock 3 Stock 1 10\% Stock 1 0.021 0.018 -0.003 Stock 2 11\% Stock 2 0.018 0.070 0.006 Stock 3 9\% Stock 3 -0.003 0.006 0.003 Target Retum 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 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 -Given that Q = order quantity, D = annual demand, C = unit cost of the item, C0 = cost per order placed, i = inventory carrying charge per unit, which of the following represents the holding cost per unit?

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 noon-1 time slot?