Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages Description/Paper Instructions
MGT 3500 Homework 2
(Due 10:45am@02/25/2020)
- [25 points] You are given the following linear programming model in algebraic form, with X1 and X2 as the decision variables: Note: Each part is independent (i.e., any change made in one problem part does not apply to any other parts).
Minimize 40X1+50X2
Subject to
2X1+3X2>=30
- X1+ X2>=20 X1>=0, X2>=0
- Graph the feasible region and label the corner point. Compute the optimal solution using any method of your choice. Justify your answer and indicate the optimal solution on your graph. [10 points]
- How does the optimal solution change if the objective function is changed to 40 X1+70 X2? [10 points]
- Now your boss tells you “I apologize, but I was just informed that the X2 coefficient is not reliable, Can you tell me how much the X2 coefficient may change, both up and down, whereby the optimal solution you reported in problem
1(a) remains optimal?” Justify your answer. [5 points]
- [35 points] The Ferguson Paper Company produces rolls of paper for cash registers, adding machines, and desk calculators. They sell three widths—1.5,
2.5, and 3.5 inches—all the same diameter. The supplier provides a standard 10-inch roll from which Ferguson must cut the various sizes. The cutting machine allows 7 cutting alternatives, namely, 7 different ways that the 10-inch roll may be divided into the various widths, as described in the table below.
Cutting Number of Rolls Alternative 1.5 inch 2.5 inch 3.5 inch 1 6 0 0 2 0 4 0 3 2 0 2 4 0 1 2 5 1 3 0 6 1 2 1
7 4 0 1
For example, cutting alternative 4 consumes 9.5 inches with one 2.5-inch roll and two 3.5-inch rolls and thus leaves ½ inch of waste that must be scrapped. Due to demand requirements, the minimum production quantities for this period are
Roll Width (inches) 1.5 2.5 3.5 Units 1000 2000 4000
To minimize costs, the company wants to minimize the total number of 10-inch rolls that are consumed during the manufacturing process.
- Based on this information, explain what are (i) the decision variables, (ii) the objective, (iii) and the constraints of the decision problem? Answer in words, not math. Explain. [5 points]
- Formulate the decision problem into a linear programming in mathematic forms. [10 points]
- Please solve your linear programming problem in Excel solver, and report the optimal solution. [10 points]
- Please identify which constraints are binding and which are non-binding. Why? Explain. [10 points]
- [40 points] Colonial Furniture produces hand-crafted colonial style furniture. Plans are now being made for the production of rocking chairs, dining room tables, and/or armoires over the next week. These products go through two stages of production (assembly and finishing). The following table gives the time required for each item to go through these two stages, the amount of wood required (fine cherry wood), and the corresponding unit profits, along with the amount of each resource available next week.
Rocking Dining Armoire Available Chair Room Table Assembly (minutes) 100 180 120 3,600 Finishing (minutes) 60 80 80 2,000 Wood (pounds) 30 180 120 4,000 Unit Profit $240 $720 $600
A linear programming model has been formulated in a spreadsheet to determine the production levels that would maximize profit. The solved spreadsheet model and corresponding sensitivity report are shown below.
Rocking Dining Room Chair Table Armoire Unit Profit $240 $720 $600 Resource Required per Unit Used Available Assembly (minutes) 100 180 120 3600 <= 3,600 Finishing (minutes) 60 80 80 2000 <= 2,000 Wood (pounds) 30 180 120 3600 <= 4,000 Rocking Dining Room Chair Table Armoire Total Profit Production Quantity 0 10 15 $16,200 Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$12 Production Quantity Chair 0 -230 240 230 1E+30 $C$12 Production Quantity Table 10 0 720 180 120 $D$12 Production Quantity Armoire 15 0 600 120 120 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$6 Assembly (minutes) Used 3600 2 3600 400 600 $E$7 Finishing (minutes) Used 2000 4.5 2000 400 400 $E$8 Wood (pounds) Used 3600 0 4000 1E+30 400
For each of the following parts, answer the question as specifically and completely as is possible without resolving the problem with solver. Please show all your steps. Note: Each part is independent (i.e., any change made in one problem part does not apply to any other parts).
- Suppose the profit per armoire decreases by $50. Will this change the optimal production quantities? What can be said about the change in total profit? [10 points]
- Suppose the profit per table decreases by $60 and the profit per armoire increases by $90. Will this change the optimal production quantities? What
can be said about the change in total profit? [10 points]
- Suppose a part-time worker in the assembly department calls in sick, so that now four fewer hours are available that day in the assembly department. How much would this affect total profit? Would it change the optimal production quantities? [10 points]
- Suppose one of the workers in the assembly department is also trained to do finishing. Would it be a good idea to have this worker shift some of his time from the assembly department to the finishing department? Indicate the rate at which this would increase or decrease total profit per minute shifted. [10 points]
RUBRIC
QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT Content (worth a maximum of 50% of the total points) Zero points: Student failed to submit the final paper. 20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. 40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. 50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. Use of Sources (worth a maximum of 20% of the total points). Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. 20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. Grammar (worth maximum of 20% of total points) Zero points: Student failed to submit the final paper. 5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors 10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors 15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. 20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free. Structure of the Paper (worth 10% of total points) Zero points: Student failed to submit the final paper. 3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6th edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6th edition requirements whatsoever. 5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6th edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements. The student also significantly writes too large or too short of and paper 7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. 10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper. GET THIS PROJECT NOW BY CLICKING ON THIS LINK TO PLACE THE ORDER
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