Exam 15: Optimization Analytics

Use the table below to answer the following questions). Qualis Investments is a private limited business that manages personal financial portfolios. The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance. Characteristics of the funds are given in the table below. Qualis Mutual Fund Data Expected Annual Return Risk Measure 1 Qualis Low-priced Stock Fund 7.23\% 11.87 2 Qualis Multinational Fund 8.42\% 12.62 3 Qualis Mid-cap Stock Fund 6.66\% 13.72 4 Qualis Mortgage Fund 2.72\% 3.37 5 Qualis Income Equity Fund 8.89\% 8.4 6 Qualis Balanced Fund 3.50\% 6.91 The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund. The total amount invested in the low-priced and multinational funds are at least 35% of the total investment. The client would like an average return of at least 6%. Assume that X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively. -If the unit profit on Graystone surfboards is increased by $10, what is the Allowable Increase for Lava surfboards?

Use the table below to answer the following questions). Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit. Pickson Luthiers Corporation Data Guitar Model Selling price/Unit Variable cost/Unit Min Sales Max Sales ScarCT 750.00 660.00 0 2500 Dela Mort 788.00 680.00 0 2000 Warax 800.00 700.00 100 1000 Invazen 850.00 800.00 80 500 Production rates units/hour) ScarCT Dela Mort Warax Invazen Hours Available Assembly - 35 25 20 220 Painting 35 20 15 10 220 Sound Testing 20 10 20 18 220 Inspection 10 12 8 5 220 Packaging 9 10 5 8 220 Use a linear optimization model based on the data to answer the following question. -According to the linear optimization model, what is the total profit for the Pickson Luthiers Corporation?

Use the table below to answer the following questions). Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis. The mill operates on a 24/7 basis. The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill. Two types of looms are used: Jaquard and Northrop. Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids. Demands, variable costs for each fabric, and production rates on the looms are given in the table below. The mill has 10 Northrop looms and 2 Jaquard looms. Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price. In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally. Remington Textiles Data Fabric Demand Jaquard Northrop Capacity Capacity Mill Cost Outsourcing yards) yards/hour) yards/hour) \/ yard) Cost \/ yard) 1 50,000 5.6 0 0.53 0.81 2 62,000 5.2 4.8 0.6 0.85 3 35,000 4.8 4.5 0.71 0.84 Answer the following questions using a linear optimization model. -According to the model, what is the total amount of Fabric 2 to be produced with Northrop?

Use the table below to answer the following questions). The Riviera Transport Company RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand. Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on. Transportation Model Data Distribution Center Plant Houston Sarn Jose Jacksorville Mernphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlarita 10.75 15.16 9.65 18.50 750 Dernand 175 325 480 950 Answer the following questions) using a linear optimization model. -According to the transportation model, which of the following is the amount shipped from Dallas to Houston?

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

Use the table below to answer the following questions). Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit. Pickson Luthiers Corporation Data Guitar Model Selling price/Unit Variable cost/Unit Min Sales Max Sales ScarCT 750.00 660.00 0 2500 Dela Mort 788.00 680.00 0 2000 Warax 800.00 700.00 100 1000 Invazen 850.00 800.00 80 500 Production rates units/hour) ScarCT Dela Mort Warax Invazen Hours Available Assembly - 35 25 20 220 Painting 35 20 15 10 220 Sound Testing 20 10 20 18 220 Inspection 10 12 8 5 220 Packaging 9 10 5 8 220 Use a linear optimization model based on the data to answer the following question. -According to the linear optimization model, what is the total hours spent for painting all the models?

Use the table below to answer the following questions). The Riviera Transport Company RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand. Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on. Transportation Model Data Distribution Center Plant Houston Sarn Jose Jacksorville Mernphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlarita 10.75 15.16 9.65 18.50 750 Dernand 175 325 480 950 Answer the following questions) using a linear optimization model. -According to the transportation model, what is the amount shipped from Atlanta to Jacksonville?

Use the table below to answer the following questions). Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis. The mill operates on a 24/7 basis. The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill. Two types of looms are used: Jaquard and Northrop. Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids. Demands, variable costs for each fabric, and production rates on the looms are given in the table below. The mill has 10 Northrop looms and 2 Jaquard looms. Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price. In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally. Remington Textiles Data Fabric Demand Jaquard Northrop Capacity Capacity Mill Cost Outsourcing yards) yards/hour) yards/hour) \/ yard) Cost \/ yard) 1 50,000 5.6 0 0.53 0.81 2 62,000 5.2 4.8 0.6 0.85 3 35,000 4.8 4.5 0.71 0.84 Answer the following questions using a linear optimization model. -According to the model, what is the total amount of Fabric 3 to be purchased?

Use the table below to answer the following questions). The Riviera Transport Company RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand. Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on. Transportation Model Data Distribution Center Plant Houston Sarn Jose Jacksorville Mernphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlarita 10.75 15.16 9.65 18.50 750 Dernand 175 325 480 950 Answer the following questions) using a linear optimization model. -According to the transportation model, what is the total cost incurred by Riviera Transport Company?

Use the table below to answer the following questions). Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit. Pickson Luthiers Corporation Data Guitar Model Selling price/Unit Variable cost/Unit Min Sales Max Sales ScarCT 750.00 660.00 0 2500 Dela Mort 788.00 680.00 0 2000 Warax 800.00 700.00 100 1000 Invazen 850.00 800.00 80 500 Production rates units/hour) ScarCT Dela Mort Warax Invazen Hours Available Assembly - 35 25 20 220 Painting 35 20 15 10 220 Sound Testing 20 10 20 18 220 Inspection 10 12 8 5 220 Packaging 9 10 5 8 220 Use a linear optimization model based on the data to answer the following question. -According to the linear optimization model, what would be the total time spent on inspecting the Dela Mort models?

Use the table below to answer the following questions). Qualis Investments is a private limited business that manages personal financial portfolios. The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance. Characteristics of the funds are given in the table below. Qualis Mutual Fund Data Expected Annual Return Risk Measure 1 Qualis Low-priced Stock Fund 7.23\% 11.87 2 Qualis Multinational Fund 8.42\% 12.62 3 Qualis Mid-cap Stock Fund 6.66\% 13.72 4 Qualis Mortgage Fund 2.72\% 3.37 5 Qualis Income Equity Fund 8.89\% 8.4 6 Qualis Balanced Fund 3.50\% 6.91 The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund. The total amount invested in the low-priced and multinational funds are at least 35% of the total investment. The client would like an average return of at least 6%. Assume that X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively. -If the unit profit on Graystone surfboards is increased by $10, what is the total profit generated?

Use the table below to answer the following questions). Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis. The mill operates on a 24/7 basis. The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill. Two types of looms are used: Jaquard and Northrop. Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids. Demands, variable costs for each fabric, and production rates on the looms are given in the table below. The mill has 10 Northrop looms and 2 Jaquard looms. Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price. In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally. Remington Textiles Data Fabric Demand Jaquard Northrop Capacity Capacity Mill Cost Outsourcing yards) yards/hour) yards/hour) \/ yard) Cost \/ yard) 1 50,000 5.6 0 0.53 0.81 2 62,000 5.2 4.8 0.6 0.85 3 35,000 4.8 4.5 0.71 0.84 Answer the following questions using a linear optimization model. -From the Sensitivity Report, which of the following would reduce the total cost by $1.568 for each additional hour of capacity for the Jaquard looms?

Use the table below to answer the following questions). Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit. Pickson Luthiers Corporation Data Guitar Model Selling price/Unit Variable cost/Unit Min Sales Max Sales ScarCT 750.00 660.00 0 2500 Dela Mort 788.00 680.00 0 2000 Warax 800.00 700.00 100 1000 Invazen 850.00 800.00 80 500 Production rates units/hour) ScarCT Dela Mort Warax Invazen Hours Available Assembly - 35 25 20 220 Painting 35 20 15 10 220 Sound Testing 20 10 20 18 220 Inspection 10 12 8 5 220 Packaging 9 10 5 8 220 Use a linear optimization model based on the data to answer the following question. -According to the linear optimization model, what is the total profit contribution by the Invazen model?

When interpreting sensitivity analysis information for changes in model parameters, all other model parameters are held constant.

Use the table below to answer the following questions). Qualis Investments is a private limited business that manages personal financial portfolios. The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance. Characteristics of the funds are given in the table below. Qualis Mutual Fund Data Expected Annual Return Risk Measure 1 Qualis Low-priced Stock Fund 7.23\% 11.87 2 Qualis Multinational Fund 8.42\% 12.62 3 Qualis Mid-cap Stock Fund 6.66\% 13.72 4 Qualis Mortgage Fund 2.72\% 3.37 5 Qualis Income Equity Fund 8.89\% 8.4 6 Qualis Balanced Fund 3.50\% 6.91 The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund. The total amount invested in the low-priced and multinational funds are at least 35% of the total investment. The client would like an average return of at least 6%. Assume that X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively. -If the unit profit on Graystone surfboards is increased by $10, what is the shadow price for the finishing hours used?

In a sensitivity report, a solution is considered an) solution if the right-hand-side value of any constraint has a zero Allowable Increase or Allowable Decrease.

Use the table below to answer the following questions). Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The table below shows the relevant data. Production rates are shown in units/hour. ScarCT is assembled elsewhere). Pickson wants to determine how many guitars to make to maximize monthly profit. Pickson Luthiers Corporation Data Guitar Model Selling price/Unit Variable cost/Unit Min Sales Max Sales ScarCT 750.00 660.00 0 2500 Dela Mort 788.00 680.00 0 2000 Warax 800.00 700.00 100 1000 Invazen 850.00 800.00 80 500 Production rates units/hour) ScarCT Dela Mort Warax Invazen Hours Available Assembly - 35 25 20 220 Painting 35 20 15 10 220 Sound Testing 20 10 20 18 220 Inspection 10 12 8 5 220 Packaging 9 10 5 8 220 Use a linear optimization model based on the data to answer the following question. -According to the linear optimization model, what is the net profit per unit on Dela Mort?

Use the table below to answer the following questions). Qualis Investments is a private limited business that manages personal financial portfolios. The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance. Characteristics of the funds are given in the table below. Qualis Mutual Fund Data Expected Annual Return Risk Measure 1 Qualis Low-priced Stock Fund 7.23\% 11.87 2 Qualis Multinational Fund 8.42\% 12.62 3 Qualis Mid-cap Stock Fund 6.66\% 13.72 4 Qualis Mortgage Fund 2.72\% 3.37 5 Qualis Income Equity Fund 8.89\% 8.4 6 Qualis Balanced Fund 3.50\% 6.91 The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund. The total amount invested in the low-priced and multinational funds are at least 35% of the total investment. The client would like an average return of at least 6%. Assume that X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively. -If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the shadow price for the finishing hours used?

How does Excel's Solver help interpret reduced cost as shadow price for bounded variables?

Use the table below to answer the following questions). The Riviera Transport Company RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand. Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on. Transportation Model Data Distribution Center Plant Houston Sarn Jose Jacksorville Mernphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlarita 10.75 15.16 9.65 18.50 750 Dernand 175 325 480 950 Answer the following questions) using a linear optimization model. -Based on the Sensitivity Report on the model, which of the following is the savings on a reduction of demand of 2 units at Jacksonville?