please follow the instruction below, it is very simple and it wont take lots of timehomework_formatting_instructions_1_.pdf ____example_for_hw_1_.pdf hw2_data.xlsxOptimization for Decision Making DNSC6251

Homework Formatting Instructions

You are required to follow the following instructions for formatting your turned-in

homework. All homework assignments must be submitted through Blackboard.

1. You must provide the formulations of the optimization models (i.e. algebraic

form of constraints, objective, and variable definitions), as well as answers

to short answer questions. You can type them, or written them down and

scan them (as long as your handwriting is clearly legible). Graphs must be

clearly legible. For example, axes should be clearly labeled and be roughly

to scale.

2. Please use the provided Excel file (if any) to begin solving the questions that

make use of Excel. In many cases, the data will already be laid out in a

useful way to start you off. Sometimes, the problem will already be partially

solved, to lead you in the right direction.

3. You will need to print out each Excel spreadsheet that you update/create as

part of the homework that you hand in. Please follow the following

instructions to produce printouts that help your work to be properly graded:

a. Make sure to always “Print Headings” of the spreadsheet so that the

column labels (e.g. A, B, C) and row labels (e.g. 1, 2, 3) are visible on

the printout. In Excel 2007, 2010, and 2013, clicking the Page Layout

tab of the ribbon and then placing a check mark in the “Print

Headings” option will do this.

If you are using Excel 2003, click the File menu, then Page Setup, go

to the Sheet tab, and place a check mark in the “Print Row and

Column Headings” box (as seen below).

b. Please print each spreadsheet twice. Once with all cells showing their

respective formulas (“formula view”), and once with the “normal

view” where the cells show the numbers that the formulas evaluate to.

In Excel 2007, 2010, and 2013, you can switch between the “formula”

view and “normal” view by clicking the Formulas tab and then

clicking the “Show Formulas” button. Alternatively, Clicking Ctrl-`

also toggles between “formula” and “normal” view (hold down the

Ctrl key and press the button with the ~ symbol on it to the left of the

1 key). Make sure that column widths are large enough so that any

formulas which are seen in the “formula view” can be fully seen onscreen (and in your printout!). Additional help on how to do this is

here: http://www.mrexcel.com/articles/show-formulas-in-cells.php

c. For each spreadsheet you solve, please copy-and-paste the Excel

Solver settings into a MS Word document which gets handed in with

your assignment. To do this, click Alt-[Print Screen] to take a picture

of the Solver settings and Paste the resulting picture in MS Word. For

example, the following is a screen capture using this method.

d. Highlight or circle the important quantities (i.e. cells that contain the

optimal solution and/or optimal value)

Once you will have done the above, build a single pdf file and submit it

through Blackboard and the link associated with the corresponding

assignment.

Glickman Electronics Example

The Glickman Electronics Company in Washington, DC, produces two products: (1) the

Glickman x-pod, a portable music player, and (2) the Glickman BlueBerry, an internet-connected

color telephone. The production process for each product is similar in that both require a certain

number of hours of electronic work and a certain number of labor-hours in the assembly

department. Each x-pod takes 4 hours of electronic work and 2 hours in the assembly shop. Each

BlueBerry requires 3 hors in electronics and 1 hour in assembly. During the current production

period, 240 hours of electronic time are available, and 100 hours of assembly department time are

available. Each x-pod sold yields a profit of $7; each BlueBerry produced may be sold for a $5

profit.

Glickman’s problem is to determine the best possible combination of x-pod and BlueBerrys

to manufacture to reach the maximum profit.

Solution:

a. Formulate the problem as a linear programming model (that is, define the variables, and

write down the objective function and all constraints mathematically).

We begin by summarizing the information needed to formulate and solve this problem. Further,

let’s introduce some simple notation for use in the objective function and constraints.

Decision Variables

X1 = number of x-pods to be produced

X2 = number of BlueBerry to be produced

Objective Function and constraints

Max ($7X1 + $5X2)

Subject to:

4X1 + 3X2 ≤ 240

2X1 + 1X2 ≤ 100

X1 , X2 ≥ 0

The objective function created this way represents the overall profit from the operation. Since

each x-pod yields a profit of $7, X1 of them yield 7X1 dollars. Similarly, each BlueBerry yields a

profit of $5, which means X2 BlueBerrys yield 5X2 dollars. The overall profit will therefore be =

$7X1 + $5X2, which is the objective function we are trying to maximize.

As for the constraints, one general relationship is that the amount of a resource used is to be less

than or equal to the amount of resource available. Both these constraints represent production

capacity restrictions and, of course, affect the total profit.

First constraint:

Electronic time used is ≤ Electronic time available.

Second constraint:

Assembly time used is ≤ Assembly time available.

For example, Glickman Electronics cannot produce 70 x-pods during the production period

because if X1 = 70, both constraints will be violated. It also cannot make X1 = 50 x-pods and Xx

= 10 BlueBerrys.

What is more, since the decision variables represent units of production, we should add a nonnegativity constraint for each variable.

b. Create a spreadsheet model for this problem and solve with Excel Solver.

Figure 1 – Solver parameters

A

1

2

3

4

5

Production

Electronic Constraint

Assembly Constraint

Objective Function

(Maximization)

B

X-PODS

(X1)

30

4

2

C

BLUEBERRYS

(X2)

40

3

1

7

5

D

E

F

240 NYC

Boston -> Chicago

NYC -> Boston

NYC -> Chicago

NYC -> LA

Chicago -> LA

Capacity

300

550

340

200

470

50

200

250

800

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