Exam 13: Linear Optimization

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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 QuantityProduced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 ProfitContribution -If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the total profit generated?

Use the following information to answer the following question(s), using the SUMPRODUCT function. Stone Age Surfboards is a small manufacturer of two types of popular high-tide surfboards, the Rockwell and the Limestone models. The manufacturing process consists of two departments: fabrication and finishing. The fabrication department has 15 skilled workers, each of whom works 5 hours per day. The finishing department has 5 workers, who also work a 5-hour shift. Each pair of Rockwell surfboards requires 3 labor hours in the fabrication department and 1.5 labor hours in finishing. The Limestone model requires 4.5 labor-hours in fabrication and 2 labor-hours in finishing. The company operates 6 days a week. It makes a per-unit profit of $60 on the Rockwell model and $75 on the Limestone model. Approximately 4.1 Rockwell models and 8.4 Limestone models are produced per day. A B C D 1 Stone Age Surfboards 2 3 Data 4 Product 5 Department Rockwell Limestone Limitation (hours) 6 Fabrication 3 4.5 75 7 Finishing 1.5 2 25 8 9 Profit/Unit \ 60.00 \ 75.00 10 11 12 Model 13 Rockwell Limestone 14 Quantity Produced 4.1 8.4 Hours Used 15 Fabrication 16 Finishing 17 18 Excess Limestone 19 Market Mixture 20 21 Total Profit 22 Profit Contribution -What is the total number of hours used for fabrication?

Which of the following best defines objective functions?

Whenever a constraint has positive slack, the shadow price is equal to one.

Use the following information to answer the question(s) 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 Cerebro 1 ManufacturingModel 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 rivets manufactured?

Explain the simplex method used by Solver.

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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 QuantityProduced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 ProfitContribution -If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the Allowable Decrease for Lava surfboards?

What are the two basic properties of a linear optimization model?

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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 QuantityProduced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 ProfitContribution -What is the total number of hours used for fabrication?

Use the following information to answer the question(s) 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 Cerebro 1 ManufacturingModel 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, .

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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 QuantityProduced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 ProfitContribution -If the unit profit on both Graystone and Lava surfboards is increased by $10, what is the shadow price for the finishing hours used?

Infeasible problems can occur when the demand requirement is higher than the available capacity.

Use the following information to answer the question(s) 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 Cerebro 1 ManufacturingModel 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 approaches provided by the Analytic Solver Platform can automatically run multiple optimizations while varying model parameters within a predefined range?

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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 QuantityProduced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 ProfitContribution -If the unit profit on Graystone surfboards is increased by $10, what is the total profit generated?

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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 QuantityProduced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 ProfitContribution -What will be the total profit contribution from Lava surfboards?

A constraint function is a function of the decision variables in the problem.

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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 QuantityProduced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 ProfitContribution -Which of the following solving methods is selected in the Solver dialog for linear and linear integer optimization problems?

Use the following information to answer the question(s) 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 Cerebro 1 ManufacturingModel 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 only plugs?

Consider the spreadsheet for Stone Age Surfboards provided below. Use this data to answer the following question(s), 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 QuantityProduced Hours Used 15 Fabrication 16 Finishing 17 18 Excess Lava 19 Market Mixture 20 21 Total Profit 22 ProfitContribution -Due to decreasing profits, if the production of Graystone surfboards is stopped, compute the total profit the firm can earn.

Use the following information to answer the question(s) 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 Cerebro 1 ManufacturingModel 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 -When a model has a unique optimal solution, it means that .