3. [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

2 X1+ X2>=20

X1>=0, X2>=0

a) 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]

b) How does the optimal solution change if the objective function is changed to

40 X1+70 X2? [10 points]

c) 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.

1) 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]

2) Formulate the decision problem into a linear programming in mathematic

forms. [10 points]

3) Please solve your linear programming problem in Excel solver, and report the

optimal solution. [10 points]

4) Please identify which constraints are binding and which are non-binding. Why?

Explain. [10 points]

5. [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

Chair

Dining

Room Table

Armoire Available

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.

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).

a. 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]

b. 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]

d. 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]

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more