Operation Research Midterm

Solve the following problem graphically (Please be neat).Draw the polytope on the x-y coordinate system (can be done either by hand or computer).Show all intersection of the polytope and identify the point (x,y coordinate) where the objective function is maximized and provide that value.

Maximize Z = 3×1 + 2×2 Subject to: 1×1 + 1×2 ? 10 8×1 + 1×2 ? 24 and x1, x2 ? 0 Solution : Point (a) is the origin (0,0) where Z(a) = 3*0 + 2*0 = 0Point (b) is the intersection of line 2 and X-axis (3,0) where Z(b) = 3*3 + 2*0 = 9 Point (c) is the intersection of line 1 and line 2 (2,8) where Z(c) = 3*2 + 2*8=22 . (Optimum Solution) Point (d) is the intersection of line 1 and Y-axis (0,10) where Z(d) = 3*0 + 2*10 = 20 Y X d a b c I II Problem 5. (30 Points) Work through the simplex method (in algebraic form) step by step to solve the following problem.

Don't use plagiarized sources. Get Your Custom Essay on
Operation Research Midterm
Get a PLAGIARISM-FREE custom essay written for you!
Order Essay

Show all work and provide the solutions for each variable at every iteration of the simplex.Maximize z = 4×1 + 3×2 + 4×3 Subject to: 2×1 + 2×2 + 1×3 ? 20 2×1 + 1×2 + 2×3 ? 14 1×1 + 1×2 + 3×3 ? 15 and x1, x2, x3 ? 0 Solution : Problem 6. (30 Points) The Weigelt Corporation has three branch plants with excess production capacity. Fortunately, the corporation has a new product ready to begin production, and all three plants have this capability, so some of the excess capacity can be used in this way. This product can be made in three sizes–large, medium, and small–that yield a net unit profit of $420, $360, and $300, respectively.Plants 1, 2, and 3 have the excess capacity to produce 750, 900, and 450 units per day of this product, respectively, regardless of the size or combination of sizes involved. The amount of available in-process storage space also imposes a limitation on the production rates of the new product.

Plants 1, 2, and 3 have 13,000, 12,000, and 5,000 square feet, respectively, of in-process storage space available for a day’s production of this product. Each unit of the large, medium, and small sizes produced per day requires 20, 15, and 12 square feet, respectively.Sales forecasts indicate that if available, 900, 1,200, and 750 units of the large, medium, and small sizes, respectively, would be sold per day. At each plant, some employees will need to be laid off unless most of the plant’s excess production capacity can be used to produce the new product. To avoid layoffs if possible, management has decided that the plants should use the same percentage of their excess capacity to produce the new product. Management wishes to know how much of each of the sizes should be produced by each of the plants to maximize profit. 1.

Formulate a linear programming model for this problem by: A.Listing and labeling all of the decision variables. B. Creating an objective function for the model. C. List all of the constraints for the model. I want a complete model, not just an Excel sheet.

2. Solve the model using Excel® solver or Open Office Solver. Give the value for each decision variable and the objective function.

Homework Paper
Calculate your paper price
Pages (550 words)
Approximate price: -

Our Advantages

Plagiarism Free Papers

All our papers are original and written from scratch. We will email you a plagiarism report alongside your completed paper once done.

Free Revisions

All papers are submitted ahead of time. We do this to allow you time to point out any area you would need revision on, and help you for free.

Free Title-page

A title page preceeds all your paper content. Here, you put all your personal information and this we give out for free.

Free Bibliography

Without a reference/bibliography page, any academic paper is incomplete and doesnt qualify for grading. We also offer this for free.

Originality & Security

At Homework Sharks, we take confidentiality seriously and all your personal information is stored safely and do not share it with third parties for any reasons whatsoever. Our work is original and we send plagiarism reports alongside every paper.

24/7 Customer Support

Our agents are online 24/7. Feel free to contact us through email or talk to our live agents.

Try it now!

Calculate the price of your order

We'll send you the first draft for approval by at
Total price:
$0.00

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

We work around the clock to see best customer experience.

Pricing

Flexible Pricing

Our prces are pocket friendly and you can do partial payments. When that is not enough, we have a free enquiry service.

Communication

Admission help & Client-Writer Contact

When you need to elaborate something further to your writer, we provide that button.

Deadlines

Paper Submission

We take deadlines seriously and our papers are submitted ahead of time. We are happy to assist you in case of any adjustments needed.

Reviews

Customer Feedback

Your feedback, good or bad is of great concern to us and we take it very seriously. We are, therefore, constantly adjusting our policies to ensure best customer/writer experience.