Exam 13: Linear Optimization

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver. 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. A B C D 1 Stone Age Surfboards 2 3 Data 4 Product 5 Department Graystone Lava Limitation hours) 6 Fabrication 2.5 4.2 74 7 Finishing 2 3.6 30 8 9 Profit/Unit \ 40.00 \ 60.00 10 11 12 Model 13 Graystone Lava 14 Quantity Produced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 Profit Contribution -What is the total profit generated?

Use the following information to answer the questions) below. Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. A B C D E F 1 Cerebro Manufacturing Model 2 3 Product Plugs Rails Rivets Clips Machine Capacity mins./year) 4 Gross margin/unit \ 0.40 \ 1.20 \ 0.80 \ 1.10 5 Minutes/unit 1 2 3 1.5 250,000 6 Gross margin/minute 7 Maximum production 8 Profit -Alternate optimal solutions exist when the .

Use the table below to answer the following questions). 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. Datherin Hides Data Sumuner 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?

Use the table below to answer the following questions). 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. Datherin Hides Data Sumuner 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?

Use the following information to answer the questions) below. Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. A B C D E F 1 Cerebro Manufacturing Model 2 3 Product Plugs Rails Rivets Clips Machine Capacity mins./year) 4 Gross margin/unit \ 0.40 \ 1.20 \ 0.80 \ 1.10 5 Minutes/unit 1 2 3 1.5 250,000 6 Gross margin/minute 7 Maximum production 8 Profit -What is the gross margin per minute of plugs manufactured?

A binding constraint is one for which the Cell Value is greater than the right-hand side of the value of the constraint.

Which of the following would be considered as an example of a proportional relationships constraint?

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver. 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. A B C D 1 Stone Age Surfboards 2 3 Data 4 Product 5 Department Graystone Lava Limitation hours) 6 Fabrication 2.5 4.2 74 7 Finishing 2 3.6 30 8 9 Profit/Unit \ 40.00 \ 60.00 10 11 12 Model 13 Graystone Lava 14 Quantity Produced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 Profit Contribution -What is the Allowable Increase for Lava surfboards produced?

Use the following information to answer the questions) below. Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. A B C D E F 1 Cerebro Manufacturing Model 2 3 Product Plugs Rails Rivets Clips Machine Capacity mins./year) 4 Gross margin/unit \ 0.40 \ 1.20 \ 0.80 \ 1.10 5 Minutes/unit 1 2 3 1.5 250,000 6 Gross margin/minute 7 Maximum production 8 Profit -An unbounded problem is one for which .

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. Transpartation 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. -Linear optimization cannot be used on problems having multiple time periods.

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver. 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. A B C D 1 Stone Age Surfboards 2 3 Data 4 Product 5 Department Graystone Lava Limitation hours) 6 Fabrication 2.5 4.2 74 7 Finishing 2 3.6 30 8 9 Profit/Unit \ 40.00 \ 60.00 10 11 12 Model 13 Graystone Lava 14 Quantity Produced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 Profit Contribution -What is the Allowable Increase in the finishing hours used?

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. Transpartation 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. -Which of the following is the objective function for cost minimization?

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following questions), using the Standard Solver. 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. A B C D 1 Stone Age Surfboards 2 3 Data 4 Product 5 Department Graystone Lava Limitation hours) 6 Fabrication 2.5 4.2 74 7 Finishing 2 3.6 30 8 9 Profit/Unit \ 40.00 \ 60.00 10 11 12 Model 13 Graystone Lava 14 Quantity Produced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 Profit Contribution -What is the Allowable Decrease in the fabrication hours used?

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. Transpartation 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. -Which of the following is the constraint for total amount shipped from Dallas?

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. -Which of the following is the constraint for investment in low-priced and multinational funds?

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 following information to answer the questions) below. Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. A B C D E F 1 Cerebro Manufacturing Model 2 3 Product Plugs Rails Rivets Clips Machine Capacity mins./year) 4 Gross margin/unit \ 0.40 \ 1.20 \ 0.80 \ 1.10 5 Minutes/unit 1 2 3 1.5 250,000 6 Gross margin/minute 7 Maximum production 8 Profit -What is the total profit generated from the manufacture of rivets?

Use the following information to answer the questions) below. Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. A B C D E F 1 Cerebro Manufacturing Model 2 3 Product Plugs Rails Rivets Clips Machine Capacity mins./year) 4 Gross margin/unit \ 0.40 \ 1.20 \ 0.80 \ 1.10 5 Minutes/unit 1 2 3 1.5 250,000 6 Gross margin/minute 7 Maximum production 8 Profit -Which of the following options is used if Solver gives an error message that linearity is not satisfied?

Use the following information to answer the questions) below. Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. A B C D E F 1 Cerebro Manufacturing Model 2 3 Product Plugs Rails Rivets Clips Machine Capacity mins./year) 4 Gross margin/unit \ 0.40 \ 1.20 \ 0.80 \ 1.10 5 Minutes/unit 1 2 3 1.5 250,000 6 Gross margin/minute 7 Maximum production 8 Profit -If a model has alternative optimal solutions, .

Use the table below to answer the following questions). 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. Datherin Hides Data Sumuner 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 summer?