Exam 14: Applications of Linear Optimization

Use the table below to answer the following question(s). 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. 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 question(s). 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. 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 for sound testing the Warax model?

Use the table below to answer the following question(s). 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 = Transportation Model Data Distribution Center Plant Houston San Jose Jacksonville Memphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlanta 10.75 15.16 9.65 18.50 750 Demand 175 325 480 950 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. Answer the following question(s)using a linear optimization model. -According to the Sensitivity Report, which of the following is true if the capacity at Atlanta is increased by 230 units?

Use the table below to answer the following question(s). 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. 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 for packaging the Invazen models?

Use the table below to answer the following question(s). 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 = Transportation Model Data Distribution Center Plant Houston San Jose Jacksonville Memphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlanta 10.75 15.16 9.65 18.50 750 Demand 175 325 480 950 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. Answer the following question(s)using a linear optimization model. -According to the transportation model, what is the amount shipped from Atlanta to Memphis?

Nonnegativity of the decision variables is an example of an explicit constraint.

Problem statements such as the amount of material used in production cannot exceed the amount available in inventory would be categorized as a ________ constraint.

Use the table below to answer the following question(s). 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. 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 question(s). Letherin Hides is a company that makes boots specifically targeting college students.Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter.Accessories that are used on the boots are purchased from a supplier for $31.66.The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06($31.66)= $1.9 per quarter (rounded figure).Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour.In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help.Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour.Each boot design takes 2 hours to complete.How should production be planned over the three quarters to minimize the combined production and inventory holding costs? The table below provides information on Letherin Hides boot design cost and production. Letherin Hides Data Summer Autumn Winter 12 13 15.5 Unit Production Cost Unit Inventory 1.9 1.9 Holding Cost 1.9 450 500 Demand 200 Use a linear optimization model based on the data to answer the following questions. -According to the linear optimization model, what is the total cost incurred by Letherin Hides for the combined seasons?

Use the table below to answer the following question(s). 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 through represents the dollar amount invested in funds 1 through 6, respectively. -Which of the following describes the constraint on the mid-cap fund?

Use the table below to answer the following question(s). 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 = Transportation Model Data Distribution Center Plant Houston San Jose Jacksonville Memphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlanta 10.75 15.16 9.65 18.50 750 Demand 175 325 480 950 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. Answer the following question(s)using a linear optimization model. -Which of the following is the objective function for cost minimization?

Use the table below to answer the following question(s). Letherin Hides is a company that makes boots specifically targeting college students.Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500 in the winter.Accessories that are used on the boots are purchased from a supplier for $31.66.The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the holding cost per item is 0.06($31.66)= $1.9 per quarter (rounded figure).Letherin Hides hires freelance art designers at part-time to craft designs during the summer, and they earn $6 per hour.In the autumn, labor is more difficult to keep, and the owner must pay $6.5 per hour to retain qualified help.Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and workers earn $7.75 per hour.Each boot design takes 2 hours to complete.How should production be planned over the three quarters to minimize the combined production and inventory holding costs? The table below provides information on Letherin Hides boot design cost and production. Letherin Hides Data Summer Autumn Winter 12 13 15.5 Unit Production Cost Unit Inventory 1.9 1.9 Holding Cost 1.9 450 500 Demand 200 Use a linear optimization model based on the data to answer the following questions. -According to the linear optimization model, what is the inventory held at the end of autumn?

Which of the following is an example of a simple bounds constraint?

The mathematical form Y ≤ 450 would be considered as representing a simple bounds constraint.

Degeneracy does not impact the interpretation of sensitivity analysis information.

Use the table below to answer the following question(s). 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 = Transportation Model Data Distribution Center Plant Houston San Jose Jacksonville Memphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlanta 10.75 15.16 9.65 18.50 750 Demand 175 325 480 950 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. Answer the following question(s)using a linear optimization model. -Which of the following gives the constraint for the demand met at a distribution center?

Use the table below to answer the following question(s). 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 = Transportation Model Data Distribution Center Plant Houston San Jose Jacksonville Memphis Capacity Dallas 13.00 15.25 10.99 18.48 1250 Atlanta 10.75 15.16 9.65 18.50 750 Demand 175 325 480 950 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. Answer the following question(s)using a linear optimization model. -Which of the following is the constraint of nonnegativity for all values of i and j?

Use the table below to answer the following question(s). 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. Use a linear optimization model based on the data to answer the following question. -According to the Sensitivity Report, by how much should the unit profit on ScarCT be reduced in order for its production to be feasible?

Use the table below to answer the following question(s). 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. Answer the following questions using a linear optimization model. -According to the model, what is the total cost incurred by Remington for producing the three fabrics?

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