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Assignment 2

Order Description
In Part 1 of your Justification Report assignment, you built up the following sections: Problem Statement, Overview of Alternatives, Criteria, and Methods. In Part 2, you will revise Part 1 based on your instructor’s suggestions and add to it the following sections: Evaluation of Alternatives, Findings and Analysis, and References.

Use the basic outline below to draft your paper. Organize your responses to each question under the following section headings:
• Evaluation of Alternatives (for Questions 1-3)
• Findings and Analysis (for Questions 4-5)
• References (for Question 6)

Using the provided template, write Part 2 of a single-spaced report in which you:
1. Include and revise the sections from Assignment 2.1 (Problem Statement, Overview of Alternatives, Criteria, and Methods) per instructor suggestions.
2. Research the two (2) alternatives (i.e. possible solutions) that you’ve identified in your Part 1 Evaluation of Alternatives section. Record bibliographic information during research.
a. Example: You might research other organizations that have attempted similar solutions to the problem you have identified and explore the results of those experiments.
3. Use what you discover in your research to evaluate each alternative by each of your five (5) criteria.
a. Example: If your research revealed that four (4) companies similar to yours increased productivity after allowing their workers to telework from home three days per week, you might conclude that one of your suggested alternatives – in this case, the option to telework from home three days per week – satisfies one of your criterion of “Productivity” as a high-potential solution to a problem you’ve identified (of decreased worker morale and productivity at Doe’s Electronics). However, additional research might frustrate a recommendation of this alternative if it is found to fall short of other criteria while a second alternative fares better. For instance, a telework alternative might be found to be too costly to implement; too frustrating for consumers who prefer daily, in-person customer service; or too divergent from the company’s brand, “Always there for you!”
4. Organize the assignment by your criteria. Explain in narrative form how each of your two (2) alternatives stacks up against your first criterion. Next, explain how each alternative stacks up against your second criterion, etc.
a. Example: An abbreviated outline of what this longer section might look like based on the above example is below (Note: Only the first two [2] of five [5] required criteria are included to give you a feel for the structure). Your researched findings, represented as circled bullets below, should be explained in two to five (2-5) sentences. Include in-text citations and follow up with References in APA style):

Evaluation of Alternatives
o Productivity
b.
? Alternative A: Telework from home three (3) days per week
o {narrate findings based on research article 1 here}
? Alternative B: Offer two (2) extra Floating Holidays to each employee per year
o {narrate findings based on research article 2 here}
o Cost
d.
? Alternative A: Telework from home three (3) days per week
o {narrate findings based on research article 1 here}
? Alternative B: Offer two extra Floating Holidays to each employee per year
?
o {narrate findings based on research article 2 here}
5. Briefly summarize in narrative form the major discoveries that emerged from the Evaluation of Alternatives section.
6. Include a chart like the ones below to illustrate at a glance:

Figure 1: Alternatives Analyzed by Criteria
Criteria Telework Option Floating Holiday Option
Productivity Very high Negligible increase
Cost Very high Moderate
Company Image Increased Negligible increase
Worker Morale Increased Negligible increase
Practicality Moderate Low
TOTAL Feasibility* of Alternatives based on Criteria? Moderate to High Low to Moderate
7.
*Feasability = Capability of an alternative being carried out with success
8. Include an APA style (6th edition) References page that documents the two (2) sources (minimum) that you used and cited in-text in your Evaluation of Alternatives section. You may use secondary resources, or you may include one primary source and one secondary source. Remember that both in-text citations and References must be included (to avoid plagiarism) whenever you are directly quoting, summarizing, or paraphrasing researched material.
Your assignment must:
• Be typed, single spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA or school-specific format. Check with your professor for any additional instructions.
• Include a cover page containing the title of the assignment, your name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.

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Assignment 2

Assignment 2
Linear Programming

1. The Scrod Manufacturing Co. produces two key items – special-purpose Widgets (W) and more generally useful Frami (F).
Management wishes to determine that mix of W & F which will maximize total Profits (P).

Data W F

Unit profit contributions $ 30 $ 20

Demand estimates (unit/week) 250 500

Average processing rates – each
product requires processing on
both machines (units/hour)

Machine #1 2 4

Machine #2 3 3
The two products compete for processing time using the same limited plant capacity. Only 160 hours are available on each of two machines (1 and 2) during each week, barring unexpected equipment breakdowns. Management has established a desired minimum production level of 200 units per week (total output: W + F) in order to maintain distribution outlets.

As a newly hired management analyst for Scrod, you have been asked to analyze the available options and recommend an appropriate product mix. Your boss has suggested that you structure a model of the underlying constrained optimization problem and test to be sure that a feasible solution exists before proceeding to analyze the alternatives. (You do not have to solve this problem; just set it up and make sure that a feasible solution exists. You should try this both with and without the demand estimates included as constraints).
2. The Ace Manufacturing Company produces two lines of its product, the super and the regular. Resource requirements for production are given in the table. There are 1,600 hours of assembly worker hours available per week, 700 hours of paint time, and 1200 hours of inspection time. Regular customers will demand at least 150 units of the regular line and at least 90 of the super line.
Profit Assembly Paint Inspection
Product Line Contribution time (hr.) time (hr.) time (hr.)

Regular 50 1.2 .8 1.5

Super 75 1.6 .5 .7

a) Formulate an LP model which the Ace Company could use to determine the optimal product mix on a weekly basis. Use two decision variables (units of regular and units of super). Suggest any feasible solution and explain what “feasible solution” means.

b) Find the optimal solution by using the graphical solution technique. What is the value of the objective function? What are the values of all variables?

c) By how many units can the demand for the super product increase before the optimal intersection point changes? Explain. For the regular product?

d) How much would it be worth to the Ace Company if it could obtain an additional hour of paint time? Of assembly time? Of inspection time? Explain fully. Show all calculations.

e) Find the upper and lower bounds for assembly time by identifying the corner points on either end of the line and substituting these points into the assembly equation. What do these bounds mean? Explain.

f) Solve this problem with LINDO or POM and verify that your answers are correct.
3. Matchpoint Company produces 3 types of tennis balls: Heavy Duty, Regular, and
Extra Duty, with a profit contribution of $24, $12, and $36 per gross (12 dozen),
respectively.
The linear programming formulation is:

Max. 24×1 + 12×2 + 36×3

Subject to: .75×1 + .75×2 + 1.5×3 < 300 (manufacturing)

.8×1 + .4×2 + .4×3 < 200 (testing)

x1 + x2 + x3 < 500 (canning)

x1, x2, x3 > 0

where x1, x2, x3 refer to Heavy Duty, Regular, and Extra Duty balls (in gross). The LINDO solution is on the following page.

a) How many balls of each type will Matchpoint product?
b) Which constraints are limiting and which are not? Explain.
c) How much would you be willing to pay for an extra man-hour of testing capacity? For how many additional man-hours of testing capacity is this marginal value valid? Why?
d) By how much would the profit contribution of Regular balls have to increase to make it profitable for Matchpoint to start producing Regular balls?
e) By how much would the profit contribution of Heavy Duty balls have to decrease before Matchpoint would find it profitable to change its production plan?
f) Matchpoint is considering producing a low-pressure ball, suited for high altitudes, called the Special Duty. Each gross of Special Duty balls would require 1 ½ and ¾ man-hours of manufacturing and testing, respectively, and would give a profit contribution of $33 per gross. Special Duty balls would be packed in the same type of cans as the other balls.

Should Matchpoint produce any of the Special duty balls? Explain; provide support for
your answer.

Max 24×1 + 12×2 + 36×3
Subject to
.75×1 + .75×2 + 1.5×3 <300
.8×1 + .4×2 + .4×3 <200
x1 + x2 + x3 < 500
end

LP OPTIMUM FOUND AT STEP 2

OBJECTIVE FUNCTION VALUE

1) 8400.000

VARIABLE VALUE REDUCED COST
X1 200.000000 0.000000
X2 0.000000 8.000000
X3 100.000000 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 21.333334
3) 0.000000 10.000000
4) 200.000000 0.000000

NO. ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 24.000000 48.000000 6.000000
X2 12.000000 8.000001 INFINITY
X3 36.000000 12.000000 24.000000

RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 300.000000 450.000000 112.500000
3 200.000000 120.000000 120.000000
4 500.000000 INFINITY 200.000000

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Comments are closed.

Assignment 2

Assignment 2
Linear Programming

1. The Scrod Manufacturing Co. produces two key items – special-purpose Widgets (W) and more generally useful Frami (F).
Management wishes to determine that mix of W & F which will maximize total Profits (P).

Data W F

Unit profit contributions $ 30 $ 20

Demand estimates (unit/week) 250 500

Average processing rates – each
product requires processing on
both machines (units/hour)

Machine #1 2 4

Machine #2 3 3
The two products compete for processing time using the same limited plant capacity. Only 160 hours are available on each of two machines (1 and 2) during each week, barring unexpected equipment breakdowns. Management has established a desired minimum production level of 200 units per week (total output: W + F) in order to maintain distribution outlets.

As a newly hired management analyst for Scrod, you have been asked to analyze the available options and recommend an appropriate product mix. Your boss has suggested that you structure a model of the underlying constrained optimization problem and test to be sure that a feasible solution exists before proceeding to analyze the alternatives. (You do not have to solve this problem; just set it up and make sure that a feasible solution exists. You should try this both with and without the demand estimates included as constraints).
2. The Ace Manufacturing Company produces two lines of its product, the super and the regular. Resource requirements for production are given in the table. There are 1,600 hours of assembly worker hours available per week, 700 hours of paint time, and 1200 hours of inspection time. Regular customers will demand at least 150 units of the regular line and at least 90 of the super line.
Profit Assembly Paint Inspection
Product Line Contribution time (hr.) time (hr.) time (hr.)

Regular 50 1.2 .8 1.5

Super 75 1.6 .5 .7

a) Formulate an LP model which the Ace Company could use to determine the optimal product mix on a weekly basis. Use two decision variables (units of regular and units of super). Suggest any feasible solution and explain what “feasible solution” means.

b) Find the optimal solution by using the graphical solution technique. What is the value of the objective function? What are the values of all variables?

c) By how many units can the demand for the super product increase before the optimal intersection point changes? Explain. For the regular product?

d) How much would it be worth to the Ace Company if it could obtain an additional hour of paint time? Of assembly time? Of inspection time? Explain fully. Show all calculations.

e) Find the upper and lower bounds for assembly time by identifying the corner points on either end of the line and substituting these points into the assembly equation. What do these bounds mean? Explain.

f) Solve this problem with LINDO or POM and verify that your answers are correct.
3. Matchpoint Company produces 3 types of tennis balls: Heavy Duty, Regular, and
Extra Duty, with a profit contribution of $24, $12, and $36 per gross (12 dozen),
respectively.
The linear programming formulation is:

Max. 24×1 + 12×2 + 36×3

Subject to: .75×1 + .75×2 + 1.5×3 < 300 (manufacturing)

.8×1 + .4×2 + .4×3 < 200 (testing)

x1 + x2 + x3 < 500 (canning)

x1, x2, x3 > 0

where x1, x2, x3 refer to Heavy Duty, Regular, and Extra Duty balls (in gross). The LINDO solution is on the following page.

a) How many balls of each type will Matchpoint product?
b) Which constraints are limiting and which are not? Explain.
c) How much would you be willing to pay for an extra man-hour of testing capacity? For how many additional man-hours of testing capacity is this marginal value valid? Why?
d) By how much would the profit contribution of Regular balls have to increase to make it profitable for Matchpoint to start producing Regular balls?
e) By how much would the profit contribution of Heavy Duty balls have to decrease before Matchpoint would find it profitable to change its production plan?
f) Matchpoint is considering producing a low-pressure ball, suited for high altitudes, called the Special Duty. Each gross of Special Duty balls would require 1 ½ and ¾ man-hours of manufacturing and testing, respectively, and would give a profit contribution of $33 per gross. Special Duty balls would be packed in the same type of cans as the other balls.

Should Matchpoint produce any of the Special duty balls? Explain; provide support for
your answer.

Max 24×1 + 12×2 + 36×3
Subject to
.75×1 + .75×2 + 1.5×3 <300
.8×1 + .4×2 + .4×3 <200
x1 + x2 + x3 < 500
end

LP OPTIMUM FOUND AT STEP 2

OBJECTIVE FUNCTION VALUE

1) 8400.000

VARIABLE VALUE REDUCED COST
X1 200.000000 0.000000
X2 0.000000 8.000000
X3 100.000000 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 21.333334
3) 0.000000 10.000000
4) 200.000000 0.000000

NO. ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 24.000000 48.000000 6.000000
X2 12.000000 8.000001 INFINITY
X3 36.000000 12.000000 24.000000

RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 300.000000 450.000000 112.500000
3 200.000000 120.000000 120.000000
4 500.000000 INFINITY 200.000000

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Comments are closed.

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