Order Description

Need help with C1,C2,C3 and D See docs

Don't use plagiarized sources. Get Your Custom Essay on

Quantitative Analysis for Business | Homework Helpers

Get an essay WRITTEN FOR YOU, Plagiarism free, and by an EXPERT!

QAT1 Task # 2

A. X is the number of units of Brand X and Y is the number of units of Brand Y sold under the most favorable conditions

Each unit of Brand X contains (1) unit of nutrient, (2) units of color, (6) unit of flavor and (10) units of Grain.

Each unit of Brand Y contains (2) units of nutrient, (1) unit of color, (1) unit of flavor and (1) unit of grain.

Equation of profit

P = 100x +12.5y

Equation for nutrient

X*1+y*2

Equation for color

X*2+y*1

Equation for flavor

X*6+y*1

Equation for Grain

X*10+y*1

1. With nutrient being in short supply no more than 500 units of nutrient can be used. With a cap on nutrient this will be a maximum constraint.

X +2Y<=500

With color being in short supply no more than 150 units of color can be used. With a cap on color this will be a maximum constraint.

2X+Y<=150

With flavor being in short supply no more than 400 units of flavor can be used. With a cap on flavor this will be a maximum constraint.

6X+y<=400

With Grain being in short supply no more than 300 units of grain can be used. With a cap on grain this will be a maximum constraint.

10X+y<=300

Therefore the four constraints are:

6x+y<=400

x+2y<=500

3x+y<=150

10x+y<=300

2. The objective function is 100x +12.5y

B. The profit line as shown in the graph passes through the point (0,200). Therefore the total profit to be made can be obtained by using x = 0 and y = 200 in the profit function.

Total profit = 100*0 +12.5*200 = $2,500.

C. Constraints are:

(1) 6x +y <=400

(2) x+2y<=500

(3) 3x+y<=150

(4) 10x+y<=300

The feasible region for the problem is given by the region formed by the intersection of the graph of flavor, nutrient, grain and the x axis. We need to calculate the profits at the four points of intersection to find the optimal point.

We calculate the point of intersection for nutrient and grain.

(10X+y<+300) * 2 = (20X +2y = 600) (x +2y = 500) = 19X = 100 or x = 100/19 = X = 5.26

Y = 300 (10*5.26) = 247.4

X = 5.26

Y = 247.4

Profit using these values for x and y is: 100 * 5.26 +12.5 * 247.4 = $3,618.50

We calculate the point of intersection for flavors and nutrients

(6x + y =400) * 2 = (12x + 2y = 800) (1x+2y =500) = 11x = 300 or x = 27.27

Y = 400- (6 * 27.27) = 236.38

Y = 236.38

X = 27.27

Profit using these values for x and y is: 100 * 27.27 + 12.5 * 236.38 = $5,681.75

We calculate the point of intersection for color and grains

(3x+y=150) * 2 = (6X +2y =300) (10x + y =300) = -4x=0 = x = 4

Y = 150 (3 * 4) = 138 = Y

Profit using values for x and y is:

100 * 4 + 12.5 * 138 = $2,125

The point of intersection for grains and x axis is: x = 300/10, y = 0

Total profit = 100 * 30 +0 = $3,000.

Therefore maximum profit occurs at the intersection point of flavors and nutrients which is the optimal solution.

1. Optimal production of Brand X is 27.27 units

2. Optimal production of Brand Y is 236.38 units

3. The feasible region was used to determine the possible solutions points. Then putting the solution points in the profit function to determine the total profit at each point. The optimal solution point was then determined which is the point that profit is optimal.

D. Using the best production levels of Brand X and Y optimal profit would be $5,681.75

Why Choose Us

Top quality papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional academic writers

We have hired a team of professional writers experienced in academic and business writing. Most of them are native speakers and PhD holders able to take care of any assignment you need help with.

Free revisions

If you feel that we missed something, send the order for a free revision. You will have 10 days to send the order for revision after you receive the final paper. You can either do it on your own after signing in to your personal account or by contacting our support.

On-time delivery

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & confidential

We use several checkers to make sure that all papers you receive are plagiarism-free. Our editors carefully go through all in-text citations. We also promise full confidentiality in all our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

You are welcome to choose your academic level and the type of your paper. Our academic experts will gladly help you with essays, case studies, research papers and other assignments.

Admissions

Admission help & business writing

You can be positive that we will be here 24/7 to help you get accepted to the Master’s program at the TOP-universities or help you get a well-paid position.

Reviews

Editing your paper

Our academic writers and editors will help you submit a well-structured and organized paper just on time. We will ensure that your final paper is of the highest quality and absolutely free of mistakes.

Reviews

Revising your paper

Our academic writers and editors will help you with unlimited number of revisions in case you need any customization of your academic papers