Exam 14: Applications of Linear Optimization

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

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Keychain Publishing is planning to release two books, simultaneously, by the same author. One is a fictional book, while the other is the author's autobiography. The details of its cost, production, and demand are given in the table below. Keychain Pub lishing Data Fictional Autobiography Cost/book \ 1.75 \ 1.50 Price/book \ 11.49 \ 9.86 Base demand 50,000 65,000 Increase/ \1 Adv. 25 35 Min. percent requirement 35\% Max. percent limitation 70\% Total Budget \ 150,000 Keychain Publishing has $150,000 available to bind books and advertise them with an objective of maximizing profit contribution. Provide the objective function for maximizing profits, along with its constraints.

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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 = 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 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 Answer the following question(s) using a linear optimization model. -According to the transportation model, which of the following is the amount shipped from Dallas to San Jose?

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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 = 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 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 Answer the following question(s) using a linear optimization model. -Which of the following is the constraint for total amount shipped from Atlanta?

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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. 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?

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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 = 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 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 Answer the following question(s) using a linear optimization model. -According to the transportation model, what is the total shipment from Dallas?

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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. 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 for packaging the Invazen models?

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List out the different types of constraints that help model formulation.

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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 Unit Production Cost 12 13 15.5 Unit Inventory Holding Cost 1.9 1.9 1.9 Demand 200 450 500 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?

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

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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 Unit Production Cost 12 13 15.5 Unit Inventory Holding Cost 1.9 1.9 1.9 Demand 200 450 500 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?

(Multiple Choice)
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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 Unit Production Cost 12 13 15.5 Unit Inventory Holding Cost 1.9 1.9 1.9 Demand 200 450 500 Use a linear optimization model based on the data to answer the following questions. -According to the linear optimization model, what is the net production for winter?

(Multiple Choice)
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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 = 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 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 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?

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

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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 = 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 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 Answer the following question(s) using a linear optimization model. -According to the transportation model, what is the total cost incurred by Riviera Transport Company?

(Multiple Choice)
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Which of the following would be considered as an example of a proportional relationships constraint?

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Problem statements such as production must be sufficient to meet promised customer orders would be categorized as a constraint.

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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 = 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 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 Answer the following question(s) using a linear optimization model. -According to the transportation model, what is the amount shipped from Atlanta to Jacksonville?

(Multiple Choice)
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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 = 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 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 Answer the following question(s) using a linear optimization model. -Which of the following is the constraint for total amount shipped from Dallas?

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What is degeneracy in linear optimization? Give an example.

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