# Modeling and Analysis Competency Demonstration Project

*label*Mathematics

*timer*Asked: Jun 30th, 2018

*account_balance_wallet*$30

**Question description**

## Instructions

The “Modeling & Analysis Competency Demonstration Project” is designed to assess your ability to use the skills in linear modeling, linear systems & programming, and counting techniques that you’ve learned in a practical real-world application. The project scenario is a small-business startup and does not focus on EVERY aspect of a small business startup, but does focus on cost optimization and profit/loss calculation and prediction through the use of linear modeling and linear programming.

Instructions:

- Access (and download if you like) the business case study (in either MS Word of PDF format) from Content > Competency Demonstration Projects > Modeling & Analysis Competency Demonstration Project in our LEO classroom.
- Perform each of the 10 required tasks to the best of your ability. Note that some of the tasks require calculations, others require linear equation construction, still others require graphing. PLEASE show all your work when doing calculations, equation construction and graphing if you want me to consider awarding partial credit! I cannot give partial credit if you don’t show your work!
- Compile your submission. Be sure your submission includes:
- Answers to the questions posed in each of the 10 tasks;
- Required graphs (2) and whatever supporting graphs you wish to include
- Whatever work supporting your answers that you wish me to consider for partial credit (of course, if you don’t submit any work and your answer is incorrect, then I’m obliged to award no credit for your answer…)

## Tutor Answer

Attached.

Last Name 1

Name

Instructor Name

Course Number

Date

Modeling and Analysis Competency Demonstration

Task 1

The following are the section relations;

Glazed Donuts ^ Creme- Filled Frosted Donuts: 27

Glazed Donuts ^ Neither Glazed nor Frosted:1418

Creme- Filled Frosted Donuts ^ Neither Glazed nor Frosted: 1391

Glazed Donuts ^ Creme- Filled Frosted Donuts ^ Neither Glazed nor Frosted: 320

Last Name 2

Task 2 (Cost Equation),

The two pairs of points are (50,809), (90,829). Calculating the equation of the line that

defines the two points;

M= 0.5

•

•

50,809). y=mx+b or 809=1/2 × 50+b, or solving for b: b=809-(1/2)(50). b=784.

(90,829). y=mx+b or 829=1/2 × 90+b, or solving for b: b=829-(1/2)(90). b=784.

The equation of the line that defines the two points is y=1/2x+784.

The cost equation is Cx=1/2x+784.

Task 3 (Cost Equation)

Since the pairs are linear, the two pairs are (30, 255), (110, 935).

M= 17/2

•

•

(30,255). y=mx+b or 255=17/2 × 30+b, or solving for b: b=255-(17/2)(30). b=0.

(110,935). y=mx+b or 935=17/2 × 110+b, or solving for b: b=935-(17/2)(110). b=0.

y=17/2x because b became zero.

Therefore, the revenue equation is R(x) =17/2x

Last Name 3

Task 4 Graphing Revenue and Cost Equations

Graph of the Revenue cost

Task 5: Break Even Determination

Fixed Costs 40000

Variable Cost Per Unit 0

Selling Price Per Unit 8.5

Expected Unit Sales 15000

Total Revenue: $7565

Total Costs: $892

Net Profit: $6673

Last Name 4

Break Even Units: 105

Task 6

If # dozen

assorted donuts

sold daily x =

76

98

112

144

Then total

daily production

cost C(x) (in $) =

822

833

840

856

And daily

total (gross)

revenue R(x) (in $)

=

646

833

952

1209.6

And net daily

operating revenue

R(x) – C(x) (in $) =

176

0

-112

-353.6

The above tables have been filled in light of the fact that Cx=1/2x+784 and R(x) =17/2x

Task 7: Identification of Constraints in the Process

Ad Process

Task

Production

Running

Cost per

# of

Internet ad

Internet

($)

ads

500

2000

Cost per

TV ad ($)

# of TV...

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