Consider the LP below P= 3x – 2y subject to x+2y <8 3x + 2y = 12
Please submit your answers in a single Excel workbook.Where a description is required, please type your description in English in a text box, or type in Word, take a snapshot, and copy and paste into the workbook.Make the workbook well organized so I may find answers easily
Question 1: Consider the LP below
P= 3x – 2y subject to x+2y <8 3x + 2y = 12
Please provide me with the working spreadsheet solution for the system of equations above and answer the following questions.
What are the values of the decision variables at the optimal solution?
What is the value of the objective function at the optimal solution?
What are the points in the x-y plane that form the feasible region?
Which constraints are binding?
What are the dual values of the constraints?
Provide me with a graphic (it is fine if it is from Zwieg) that captures the feasible region.
Provide the Excel Sensitivity Analytics Output and the Answers Output
What is the slope of the objective function?
What is the range of feasibility?
What is the range of optimality?
Interpret the shadow prices for the constraints. For a one unit change what do they imply?
If we change the objective function to a minimization, what is the value of the decision variables at the new optimal solution.
What is the value of the objective function at the new optimal solution?
Question 2: Mel’s Two Wheelers
Mel’s Two Wheeler Bikes is introducing two new bicycle frames, the Roadie and the Road Warrior, to be made from special aluminum and steel alloys.The anticipated unit profits are $275 for the Deluxe and $350 for the Professional. The number of pounds of each alloy needed per frame is summarized in the table below
Bike
Aluminum Alloy
Steel Alloy
Roadie
2
3
Road Warrior
4
2
A supplier delivers 100 pounds of the aluminum alloy and 80 pounds of the steel alloy, weekly.
Write out the LP to solve this problem.
What is the value of the decision variables at the optimal solution (meaning, wow many Roadie and Road Warrior frames should Mel’s produce each week?)
What is the projected profitability for Mel’s weekly based on this optimization (meaning what is the value of the objective function at the optimal solution?)
What are the points in the x-y plane that form the feasible region?
Which constraints are binding?
What are the dual values of the constraints?
Provide me with a graphic (it is fine if it is from Zwieg) that captures the feasible region.
Provide the Excel Sensitivity Analytics Output and the Answers Output
What is the slope of the objective function?
What is the range of feasibility?
What is the range of optimality?
Interpret the shadow prices for the constraints. For a one unit change what do they imply?
If we change the objective function to a minimization, what is the value of the decision variables at the new optimal solution?
What is the value of the objective function at the new optimal solution?
Provide the implementation in Excel.
What is the optimal solution (decision variables) and value of the objective function for maximization of profit?
What is the range of optimality for the objective function?
What is the range of feasibility for each of the constraints?
Which constraints are binding?
Question 3: Par Inc. Revisited for 3 decision variables
Replicate Par inc with 3 golf bags introduced using the following setup of the model
Question 4: Foster
The transportation problem for Foster as discussed in class and the text and presentation has this representation in the Figure 1.
Figure 1: Foster
The optimal solution for the objective function was framed as a minimization problem.I reviewed two methods to do the optimization. The first way largely mimics translating the mathematics into a set of stacked expressions and translates those stacked expressions into a spreadsheet that groups the decision variables as a ‘block’ (matrix), the coefficients as a ‘block’ (matrix) and the RHS values of the constraints as a column (vector).The second way I find somewhat less direct, but it is nevertheless explained well in the book and my class.Using either implementation, reconsider the problem making the following changes to costs on the arcs in the table below (Everything else is unchanged.).
What is the optimal solution? Provide me with the minimization value for the objective function as well as a summary table with the new distribution values along the routes (the supply of generators distributed to the demand nodes as shown in class and the book).
Analyze with arcs as costs (a few written sentences, max 1 paragraph supported by a table) on business decisions backed by your optimization work on the supply and demand and costs for specific cities of interest. For example total costs per city and their differences might be a good place to start. Is satisfying demand in all cities equally efficient from a business perspective, for example?
Interpret the values on the arcs as profits.Then, re-solve.Provide me with the maximized value for the objective function as well as a summary table with the new values for the routes (supply distributed to demand nodes) as in the table above.
Analyze with arcs as profits. a few written sentences, max 1 paragraphs supported by a table) on business decisions backed by your optimization work on the supply and demand and costs for specific cities of interest. For example total costs per city and their differences might be a good place to start. Is satisfying demand in all cities equally efficient from a business perspective, for example?
Question 5: Ryan
Figure 2 depicts the network diagram for Transhipment of Ryan Electronics.
Figure 2: Ryan
Shown are supply, demand, arc costs, and connects between nodes. Replicate this problem with the following change to the values of the arcs in shown in the table below (and no other changes to route structure or supply demand values for the nodes
What is the optimal solution? Provide me with the minimization value for the objective function as well as a summary table with the new distribution values along the routes (the supply of electronics distributed to the demand nodes as shown in class and the book).
Analyze with arcs as costs (a few written sentences, max 1 paragraphs supported by a table) on business decisions backed by your optimization work on the supply and demand and costs for specific cities of interest. For example total costs per city and their differences might be a good place to start.
A tornado from the land of OZ is going to hit Kansas City. It’s a magic storm such that the only way out of Kansas City is via a new path from Kansas City to New Orleans with an arc cost of 10. All other routes out of Kansas City are eliminated, temporarily, because of the tornado. With this new added constraint, Provide me with the minimization value for the objective function as well as a summary table with the new distribution values along the routes.
Going back to the casting of the problem with the new table above (without the restrictions discussed in 2.c on KansasCity outflows an no new route to New Orleans), interpret the values on the arcs as profits.Then, resolve.Provide me with the maximized value for the objective function as well as a summary table with the new values for the routes (supply distributed to demand nodes) as in the table above.
Analyze with arcs as profits. a few written sentences, max 1 paragraphs supported by a table) on business decisions backed by your optimization work on the supply and demand and costs for specific cities of interest.
Requirements: 500
Please submit your answers in a single Excel workbook. Where a description is required, please type your description in English in a text box, or type in Word, take a snapshot, and copy and paste into the workbook. Make the workbook well organized so I may find answers easily
Question 1: Consider the LP below
Please provide me with the working spreadsheet solution for the system of equations above and answer the following questions.
What are the values of the decision variables at the optimal solution?
What is the value of the objective function at the optimal solution?
What are the points in the x-y plane that form the feasible region?
Which constraints are binding?
What are the dual values of the constraints?
Provide me with a graphic (it is fine if it is from Zwieg) that captures the feasible region.
Provide the Excel Sensitivity Analytics Output and the Answers Output
What is the slope of the objective function?
What is the range of feasibility?
What is the range of optimality?
Interpret the shadow prices for the constraints. For a one unit change what do they imply?
If we change the objective function to a minimization, what is the value of the decision variables at the new optimal solution.
What is the value of the objective function at the new optimal solution?
Question 2: Mel’s Two Wheelers
Mel’s Two Wheeler Bikes is introducing two new bicycle frames, the Roadie and the Road Warrior, to be made from special aluminum and steel alloys. The anticipated unit profits are $275 for the Deluxe and $350 for the Professional. The number of pounds of each alloy needed per frame is summarized in the table below
A supplier delivers 100 pounds of the aluminum alloy and 80 pounds of the steel alloy, weekly.
Write out the LP to solve this problem.
What is the value of the decision variables at the optimal solution (meaning, wow many Roadie and Road Warrior frames should Mel’s produce each week?)
What is the projected profitability for Mel’s weekly based on this optimization (meaning what is the value of the objective function at the optimal solution?)
What are the points in the x-y plane that form the feasible region?
Which constraints are binding?
What are the dual values of the constraints?
Provide me with a graphic (it is fine if it is from Zwieg) that captures the feasible region.
Provide the Excel Sensitivity Analytics Output and the Answers Output
What is the slope of the objective function?
What is the range of feasibility?
What is the range of optimality?
Interpret the shadow prices for the constraints. For a one unit change what do they imply?
If we change the objective function to a minimization, what is the value of the decision variables at the new optimal solution?
What is the value of the objective function at the new optimal solution?
Question 3: Par Inc. Revisited for 3 decision variables
Replicate Par inc with 3 golf bags introduced using the following setup of the model
Provide the implementation in Excel.
What is the optimal solution (decision variables) and value of the objective function for maximization of profit?
What is the range of optimality for the objective function?
What is the range of feasibility for each of the constraints?
Which constraints are binding?
Question 4: Foster
The transportation problem for Foster as discussed in class and the text and presentation has this representation in the Figure 1.
Figure 1: Foster
The optimal solution for the objective function was framed as a minimization problem. I reviewed two methods to do the optimization. The first way largely mimics translating the mathematics into a set of stacked expressions and translates those stacked expressions into a spreadsheet that groups the decision variables as a ‘block’ (matrix), the coefficients as a ‘block’ (matrix) and the RHS values of the constraints as a column (vector). The second way I find somewhat less direct, but it is nevertheless explained well in the book and my class. Using either implementation, reconsider the problem making the following changes to costs on the arcs in the table below (Everything else is unchanged.).
What is the optimal solution? Provide me with the minimization value for the objective function as well as a summary table with the new distribution values along the routes (the supply of generators distributed to the demand nodes as shown in class and the book).
Analyze with arcs as costs (a few written sentences, max 1 paragraph supported by a table) on business decisions backed by your optimization work on the supply and demand and costs for specific cities of interest. For example total costs per city and their differences might be a good place to start. Is satisfying demand in all cities equally efficient from a business perspective, for example?
Interpret the values on the arcs as profits. Then, re-solve. Provide me with the maximized value for the objective function as well as a summary table with the new values for the routes (supply distributed to demand nodes) as in the table above.
Analyze with arcs as profits. a few written sentences, max 1 paragraphs supported by a table) on business decisions backed by your optimization work on the supply and demand and costs for specific cities of interest. For example total costs per city and their differences might be a good place to start. Is satisfying demand in all cities equally efficient from a business perspective, for example?
Question 5: Ryan
Figure 2 depicts the network diagram for Transhipment of Ryan Electronics.
Figure 2: Ryan
Shown are supply, demand, arc costs, and connects between nodes. Replicate this problem with the following change to the values of the arcs in shown in the table below (and no other changes to route structure or supply demand values for the nodes
What is the optimal solution? Provide me with the minimization value for the objective function as well as a summary table with the new distribution values along the routes (the supply of electronics distributed to the demand nodes as shown in class and the book).
Analyze with arcs as costs (a few written sentences, max 1 paragraphs supported by a table) on business decisions backed by your optimization work on the supply and demand and costs for specific cities of interest. For example total costs per city and their differences might be a good place to start.
A tornado from the land of OZ is going to hit Kansas City. It’s a magic storm such that the only way out of Kansas City is via a new path from Kansas City to New Orleans with an arc cost of 10. All other routes out of Kansas City are eliminated, temporarily, because of the tornado. With this new added constraint, Provide me with the minimization value for the objective function as well as a summary table with the new distribution values along the routes.
Going back to the casting of the problem with the new table above (without the restrictions discussed in 2.c on Kansas City outflows an no new route to New Orleans), interpret the values on the arcs as profits. Then, resolve. Provide me with the maximized value for the objective function as well as a summary table with the new values for the routes (supply distributed to demand nodes) as in the table above.
Analyze with arcs as profits. a few written sentences, max 1 paragraphs supported by a table) on business decisions backed by your optimization work on the supply and demand and costs for specific cities of interest.
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