Finite Math Written Optimization Analysis (part 2)

Written Optimization Analysis (part 2)( Due: Mon, 24 Jun | Status: Not Completed )This assignment requires you to analyze and solve an optimization problem presented in an e-mail style format. Download the attached Optimization word problem and read through the scenario.Note: This is the same problem started in the “Written Optimization Setup” graded discussion.Written AssignmentAfter you have analyzed the scenario, solve the optimization problems set up earlier in the week and determine the optimal solution. You will solve the problems using graphical and computational methods (Excel). Directions on required resources are available at the bottom.Then draft a response to the questions posed in each problem, describing the results of your analysis. NOTE: Write your response in a professional manner, as if submitting your analysis to a supervisor. Submit your completed analysis in this assignment.Include a graph along with your solution for problem 1.Include the results from Excel spreadsheet with the values clearly labeled for problem 2.(These can be included within the written response, or as separate files)Please zip your written report and any and all associated files into a single file and upload that to this assignment.Naming Convention:  yourLastname-Optimization-MMYY.zipUse your last name, not “yourLastname”.MM is the two digit month, YY is the last two digits of the year. ————————————-There are a few ways in which you can generate a graph.  Please see the associated videos for more information.1)Grapher application in the Utilities folder (within the Applications folder)2)Download the free, open source, dynamic mathematical software Geogebra available at: http://www.geogebra.org/

Q.1

Suppose Console game is represented by variable X

And the mobile game is represented by variable Y

We need to maximize Profit by selling these games so our

Profit function becomes P = 3.6 x + 2.0 y

As given in chart the manpower hours required at various levels is

Console Game Mobile Game

Development 10920 7280

Art 13000 2600

Management 2080 2600

Design 3120 9360

Also we are given the max man-hours based on our current staff

Development 123,760

Art 117,000

Design 93,600

Management 29,640

Using the above table and the max man-hours available we can write the constraints for manufacture of both the games

10920x + 7280y ≤ 123760

13000x + 2600y ≤ 117000

2080x + 2600y ≤ 93600

3120x + 9360y ≤ 29640

 x >= 0, y >= 0

Question 2

Q.2

Suppose Console game is represented by variable X1

the mobile game is represented by variable X2

and the PC game is represented by variable X3

We need to maximize Profit by selling these games so our

Profit function becomes P = 3.6 c + 2.0 m + 2.8p

As given in chart the manpower hours required at various levels is

Console Game Mobile Game PC Game

Development 10920 7280 9360

Art 13000 2600 8840

Management 2080 2600 1560

Design 3120 9360 5720

Also we are given the max man-hours based on our current staff

Development 123,760 + 44 X 520 = 123,760 + 22,880 = 146,640

Art 117,000 + 58 X 520 = 117,000 + 30,160 = 147,160

Design 93,600

Management 29,640 + 2 X 520 = 29,640 + 1,040 = 30,680

Using the above table and the max man-hours available we can write the constraints for manufacture of both the games

10920×1 + 7280×2 + 9360×3 ≤ 146640

13000×1 + 2600×2 + 8840×3 ≤ 147160

2080×1 + 2600×2 + 1560×3 ≤ 30680

3120×1 + 9360×2 +5720×3 ≤ 93600

X1, X2, X3 ≥ 0

Color coded

≤
≤
≤

X1 X2 X3

Problem Name:

Variables

X1

X2

X3

Sign

RHS

LHS

Slack

=

Max/Min

≤

Solutions

Created By:

Activity per cell

Enter a text into these locations, usually a label

Enter a number into these locations, from your

Variable values stored here. NOTHING TO INPUT

Formulas entered here

Helpful labels for the spreadsheet.

Not used in the problem

NOTE

All info for this spreadsheet is established

in part one of the assignment.

Please reference your work in the Written

Optimization Setup Graded Discussion

Bla

nk

Setup

Problem Name:

Variables X1 X2 X3 Sign RHS LHS Slack
= Max/Min
≤
≤
≤
≤

X1 X2 X3

Created By:

Blank

Bla

Color coded

≤
≤
≤

X Y

Problem Name:

Variables

X

Y

Sign

RHS

LHS

Slack

=

Max/Min

≤

Solutions

Created By:

Activity per cell

Enter a text into these locations, usually a label

Enter a number into these locations, from your

Variable values stored here. NOTHING TO INPUT

Formulas entered here

Helpful labels for the spreadsheet.

Not used in the problem

NOTE

All info for this spreadsheet is established

in part one of the assignment.

Please reference your work in the Written

Optimization Setup Graded Discussion

Bla

nk

Setup

Problem Name:

Variables X Y Sign RHS LHS Slack
= Max/Min
≤
≤
≤
≤

X Y

Created By:

Blank

Bla

To: Software Development Team Leaders
From: Robert Hofmann
Date: 12 December
Re: Written Optimization Analysis

M e s s a g e
The state has created new legislation about “crunch-time”, and as such requires us to adjust our
projects for the next quarter. So for the next 13 weeks we will assume that there will be no
scheduled overtime. Our adjusted budget for the quarter gives us 520 hours to schedule per
employee (13 weeks x 40 hours per week = 520 total hours).

We have to determine how many projects we can complete during this time period, making
adjustments based on the man-hours worked on previous projects. Please figure out the
number of game we can make of each type that yields the highest profit.

Additional Information and the projected profit and estimated man-hours based on previous
projects are presented in the following pages pages.

Q u a r t e r l y P r o j e c t i o n
U p d a t e

Written Optimization Report:
Problem 1

To create a single console game, we previously required 10,920 man-hours of development,
13,000 man-hours on art, 3,120 man-hours for design, and 2,080 man-hours for production
management. The projected profit for console game titles is $3.6 million each.

The work requirements for a mobile game are quite a bit different: 7,280 man-hours in
development, 2,600 man-hours art, 9,360man-hours in design, and 2,600 man-hours in
production management. The projected profit for handheld game titles is $2 million each.

Our current staff consists of 238 programmers, 225 artists, 180 designers, and 57 production
managers.

This should give us:

§ 123,760 man-hours in the development pool (238 x 520 = 123,760)
§ 117,000 man-hours in the art pool (225 x 520 = 117,000),
§ 93,600 man-hours in the design pool (180 x 520 = 93,600), and
§ 29,640 man-hours in management (57 x 520 = 29,640)

to allocate to projects,

Department
  Console
 Game
  Mobile
 Game
 
Development
  10,920
 man-­‐hours
  7,280
 man-­‐hours
 
Art
  13,000
 man-­‐hours
  2,600
 man-­‐hours
 
Management
  2,080
 man-­‐hours
  2,600
 man-­‐hours
 
Design
  3,120
 man-­‐hours
  9,360
 man-­‐hours
 

 
 
 Profit
 
Projection
 
 $3,600,000
 
 
 $2,000,000
 
 

Figure out how many console and mobile games can be made this quarter to maximize
our profit. In addition, report what pools (development, artists, designers, and
managers) have some unutilized employees, and which pools could be expanded to
increase profits.

Note: If you want to analyze this problem in terms of number of people on each project, you will
need to convert from man-hours to number of people. Divide the number of man-hours by 520
hours to determine the number of people needed to complete the work in 13 weeks.

Written Optimization Report:
Problem 2

We have decided to expand and create a new PC games department. Out projections indicate
PC game titles will make $2.8 million in profit each. The work requirements are 9,360 man-
hours for development, 8,840 man-hours on artwork, 5,720 man-hours for design, and 1,560
man-hours for production management.

Department
  Console
 Game
  Mobile
 Game
  PC
 Game
 
Development
  10,920
 man-­‐hours
  7,280
 man-­‐hours
  9,360
 man-­‐hours
 
Art
  13,000
 man-­‐hours
  2,600
 man-­‐hours
  8,840
 man-­‐hours
 
Management
  2,080
 man-­‐hours
  2,600
 man-­‐hours
  1,560
 man-­‐hours
 
Design
  3,120
 man-­‐hours
  9,360
 man-­‐hours
  5,720
 man-­‐hours
 

 
 
 
 Profit
 
Projection
 
 $3,600,000
 
 
 $2,000,000
 
 
 $2,800,000
 
 

To help staff this department, we hired 44 more programmers for the development team, 58
more artists for the art team, and 2 more managers for the management team. Please adjust
the total man-hours available based on this new staff before calculating the new estimations.

Figure out how many console, PC, and mobile games can be made this quarter to
maximize our profit. In addition, report what pools (development, artists, designers, and
managers) have some unutilized employees, and which pools could be expanded to
increase profits.