IENG2201: Mathematical Models for Business Decision Making - Accounting and Finance Assignment Help

Assignment Task

For this assignment, you will be given a series of scenarios explained in writing and asked to translate them into a mathematical model: both in terms of written equations as well as in Excel. You will be asked to find at least 1 VALID solution to each model, but DO NOT try to solve your mathematical models to find the optimal solution. In the future, you will take courses such as Operations Research I & Operations Research II that will deal extensively with solution methods and best practices.

Q1

Jylan runs a small consulting business. Currently, there are four client projects on the agenda, and they have to decide who to assign to each project. There are 5 employees available without a currently assigned project, Jane, Jen, Jim, John, and June. Each has their own strengths and weaknesses in different areas.

Jylan wants to maximize the expected performance across all four projects, with each employee only being able to be assigned to a single project and vice versa. They have complied a table of how well each employee is expected to perform on each of the projects based on their past performance with projects of a similar nature.

1. Formulate this problem as a linear model. Write out the equations of the objective function and all constraints. Remember to define your decision variables and parameters and explain what the objective function and each constraint is meant to do.
2. Represent this linear model on an Excel spreadsheet.
3. Using the Excel model, guess and test a valid solution (i.e., doesn’t break any constraints). You do not need to find the optimal solution.
4. Interpret your solution. Who is assigned to which project? What is the average expected performance across all four projects? Do you think this is the best that could be achieved?

Q2

A company currently has five different production centers and four different distribution centers. The company works off of a pull system, and so every month the distribution centers put in an order for how much product they will need, and the production centers will produce the product and send it to them. This demand MUST be met.

It costs a lot of money to move the product so naturally the company wants to try and minimize the distance traveled as much as possible. The distance matrix between the production and distribution centers is provided below. A production center can send product to multiple distribution centers as needed, however each production center has only a certain capacity each month to produce product. Additionally, distribution centers can receive product from multiple production centers if required.

1. Formulate this problem as a linear model. Write out the equations of the objective function and all constraints. Remember to define your decision variables and parameters and explain what the objective function and each constraint is meant to do.
2. Represent this linear model on an Excel spreadsheet.
3. Using the Excel model, guess and test a valid solution (i.e., doesn’t break any constraints). You do not need to find the optimal solution.
4. Interpret your solution. What is the total distance the product will need to travel? How much product is being sent from production center X to distribution center Y (list all non-zero x,y combinations)?
5. Consider a situation where the company doesn’t want any of their production centers to sit idle. To prevent this, they make it a requirement that each production center produce and ship at least 5 units of goods each month, regardless of whether it will hurt the shipping distance or not. What additional constraint would you need to add to the model to enforce this new requirement? You do not need to remake the model in Excel again, just write out this new constraint set and explain how it works.

Q3

Farmers are trying to decide how much of each crop to plant to maximize their revenue. They have five different plots of land scattered around the county. Each plot of land has a different amount of water allocation budget (how much water from local water sources such as wells, aquifers, or rivers, they are able / allowed to use to irrigate their fields). The farmers are considering four different crops for planting in the fields: corn, oats, rice, and potatoes. Each crop has its own water requirements and revenue per acre of the crop planted. Each field can have any combination of the crops planted in it, so long as it doesn’t exceed the land or water allocation. Finally, there is only so much demand for each type of crop, and so we assume that producing more of a crop than there is demand for will result in no additional revenue.

1. Formulate this problem as a linear model. Write out the equations of the objective function and all constraints. Remember to define your decision variables and parameters and explain what the objective function and each constraint is meant to do.
2. Represent this linear model on an Excel spreadsheet.
3. Using the Excel model, guess and test a valid solution (i.e., doesn’t break any constraints). You do not need to find the optimal solution.
4. Interpret your solution. What is the expected revenue for the farmers with your solution? What is the allocation of crops amongst the fields?
5. Consider a scenario where for whatever mix of crops the farmers decide to plant, no crop is allowed to make up more than 50% of the total acreage planted. They don’t want to flood the market with one type of crop. What additional constraint would you need to add to the model to enforce this new requirement? Is there anything different about this constraint compared to previous constraints? You do not need to remake the model in Excel or solve it again, just write out this new constraint set and explain how it works.

Q4

A company is trying to decide which of five different factories they should build to maximize profit from manufacturing and selling three different products.

Each factory has an associated cost to build and will be able to produce any combination of each of the three products. However, due to local factors, the cost to produce a product at each factory will be different, and each factory will have a limited capacity of the total number of products of any kind that they can make (i.e., if the max capacity is 50, you can produce 20 of product 1, 30 of product 2, and 0 of product 3).

Each product has its own market demand and sale price. Producing more of a product then there is demand for results in no additional profit. Additionally, not all demand needs to be met (i.e., if plant 2,3, and 4 made 75 of product 1 at a profit, but getting plant 1 to make the remaining 25 would yield a loss, they won’t make those remaining 25 products).

1. Formulate this problem as a linear model. Write out the equations of the objective function and all constraints. Remember to define your decision variables and parameters and explain what the objective function and each constraint is meant to do.
2. Represent this linear model on an Excel spreadsheet.
3. Using the Excel model, guess and test a valid solution (i.e., doesn’t break any constraints). You do not need to find the optimal solution.
4. Interpret your solution. What is the expected profit for the company with your solution? Which factories are open? How many of each product does each factory make? Are you capturing all the demand?

This IENG2201 - Accounting and Finance has been solved by our Phd Experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing Style. Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered.

You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turn tin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.