Linear Programming Case Study - Assignment 1

profileMathematicsExpert
 (Not rated)
 (Not rated)
Chat

Assignment 1.  Linear Programming Case Study 

 

 A beauty salon tries to determine how many bottles of fire red nail polish, bright red nail polish, basil green nail polish, and basic pink nail polish to stock. The profits for each nail polish; assumming that every piece stocked will be sold, are as follows: $100 per bottle of fire red nail polish, $120 per bottle of bright red nail polish, $150 per bottle of basil green nail polish, and $125 per bottle of basic pink nail polish. The display space and set up time requirements are listed in the table. Note that green nail polish does not require any time to prepare its display.

  

Display requirements

fire red

bright red

basil green

basic pink

available

Display space (units)

1

2

2

2

108

Time to set up a display (minutes)

3

5

 

1

120

 

The maximum demand combined for fire red and green polish is 25 bottles, while the minimum demand combined for bright red, green and pink nail polish bottles is at least 50 bottles.

 

a)      Formulate the Linear Programming model for this problem

 

b)      Solve the problem using Excel Solver or QM for Windows

 

c)      How many bottles of fire red nail polish, bright red nail polish, basil green polish and pink nail polish should be stocked?  

 

d)      What is the maximum profit?

 

e)      How much space will be left unused?

 

f)       How many minutes of idle time remaining for setting up the display?

 

g)      To what value can the per bottle profit on fire red nail polish drop before the solution would change?

 

h)      By how much can the per bottle profit on green basil nail polish increase before the solution would change?

 

i)      Is it possible for saloon to increase the profit by getting more display space or using more time for setting up the displays?

 

 

Please turning in two (2) deliverables, a short writeup of the project and the spreadsheet or QM for Windows file showing your work.

 

 Write up.  

 

Your write up should introduce your solution to the project by describing the problem.  Correctly identify what type of problem this is.  For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model.  This should be encapsulated in one (1) or two (2) succinct paragraphs.  

 

After the introductory paragraph, write out the L.P. model for the problem.  Include the objective function and all constraints, including any non-negativity constraints.  Then, you should present the optimal solution, based on your work in Excel/QM for Windows. Explain what the results mean.  

 

Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price. 

 

Excel/ QM for Windows

 

Please set up your problem in Excel and find the solution using Solver or solve the problem using QM for Windows. Turn in the entire spreadsheet, showing the setup of the model, and the results or turn in the entire QM for Windows file (not the printscreen). 

 

Your work will be graded according to the following rubric. 

 

Points: 110

Assignment 1:  Linear Programming Case Study

Criteria

 

Unacceptable

Below 60% F

Meets Minimum Expectations

60-69% D

 

Fair

70-79% C

 

Proficient

80-89% B

 

Exemplary

90-100% A

Explain what type of problem this is and the approach you are taking (20%)

Did not explain what type of problem this is and the approach taken, or did so insufficiently.

Insufficiently explained what type of problem this is and the approach taken

Partially explained what type of problem this is and the approach taken

Satisfactorily explained what type of problem this is and the approach taken

Thoroughly explained what type of problem this is and the approach taken

 

Objective function specified correctly in writeup (10%)

Objective function is specified incorrectly, with both coefficients incorrect or missing. 

Objective function is specified, but one (1) coefficient is incorrect.

Coefficients for objective function are correct, but whether this is a max or min problem is incorrect.

 

Objective function is specified correctly.

Constraints are specified correctly in writeup (10%)

Constraints are specified incorrectly or missing.

Some constraints are correctly specified.

Most constraints are correctly specified.

  All constraints are correctly specified, buy applicable nonnegativity constraints are omitted.

  All constraints are correctly specified, including nonnegativity constraints, if applicable.

Specified L.P. Model is correctly translated to Excel (10%)

Specified L.P. Model is incorrectly translated into Excel

Specified model is translated to Excel in a partially correct manner

Specified model is translated to Excel in a mostly correct manner

 

Specified model is correctly translated to Excel

Correct Answer is Obtained (10%)

Correct optimum is not obtained

 

 

 

Correct optimum is obtained

Correctly answer the sensitivity analysis part of the problem. (15%)

Did not attempt the sensitivity analysis part of the problem or did so with less than 60% accuracy and completeness

Insufficiently explained and/or  provided a partially correct answer to the sensitivity analysis part of the problem

Partially explained and/or provided a partially correct answer to the sensitivity analysis part of the problem

Satisfactorily explained and correctly answered the sensitivity analysis part of the problem

Thoroughly explained and correctly answered the sensitivity analysis part of the problem

Correctly answer the shadow price part of the problem.  (15%)

Did not attempt the sensitivity analysis part of the problem or did so with less than 60% accuracy and completeness

Insufficiently explained and/or  provided a partially correct answer to the sensitivity analysis part of the problem

Partially explained and/or provided a partially correct answer to the sensitivity analysis part of the problem

Satisfactorily explained and correctly answered the sensitivity analysis part of the problem

Thoroughly explained and correctly answered the sensitivity analysis part of the problem

5. Writing / Grammar and mechanics

(10%)

Serious and persistent errors in grammar, spelling, and punctuation.

Numerous errors in grammar, spelling, and punctuation.

Partially free of errors in grammar, spelling, and punctuation.

Mostly free of errors in grammar, spelling, and punctuation.

Free of errors in grammar, spelling, and punctuation.

 

 

 

  • 9 years ago
A+ Grade Complete Solution (Text & EXCEL)
NOT RATED

Purchase the answer to view it

blurred-text
  • attachment
    case_study.docx
  • attachment
    linear_programming_case_study.xlsx