Invent a company of your own or do Internet research to identify a company you would like to do a case study of. Make sure to select a company to which you can apply the techniques you learned in this chapter. Example: You could select a small, local, landscaping company. Identify one product or service the company sells. Identify the company's primary costs, and estimate the company's unit profit for that product or service. Conduct a break-even analysis if the company sold only that product or service. Write a paragraph about how varying parameters such as fixed costs, variable costs, and unit profit affect the break-even analysis. Example: You could choose a gutter cleaning service. Fixed costs include equipment and trucks. Each gutter cleaning has a certain price to cover costs of labor and materials for that single cleaning. Identify a business decision this company should consider. Decision tree and examine the situation. What would happen if the market gets stronger or weaker? Calculate expected returns from various possibilities. Determine the best course of action and write a paragraph explaining your reasoning. Example: You could decision tree whether to invest in a better mower, in more advertising, or in a new employee.  Project schedule for a business service or product. Identify the steps of the project and their dependencies. Estimate times and costs for those steps. Create a CPM/PERT network and find the critical path. Identify places where there is slack time. Which parts of the project may need to be crashed? How long is the project expected to take? Record your findings and write two paragraphs explaining your reasoning behind the schedule. Identify what you found out by doing your analyses. Example: You could schedule for landscaping work on a customer's yard. Plans and drawings need to be made. Materials need to be purchased. Different parts of the yard may need to be dug up, while work can begin on others right away. But remember that you can't drive earthmoving machinery out over the finished product! Identify a linear programming problem for your business. Set up an equation and a set of constraints and solve to determine the optimal solution. Write a paragraph discussing your solution method and what you found. Discuss how changes in the linear programming equation and constraints would change your solution. Example: You could determine the optimal mix of lawn mowing and gutter cleaning tasks to fit your company's labor. Constraints would include the number of man-hours available, the number required for each task, and the numbers of tasks that are available to do any given week.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Invent a company of your own or do Internet research to identify a company you would like to do a case study of. Make sure to select a company to which you can apply the techniques you learned in this chapter.

Example: You could select a small, local, landscaping company.

Identify one product or service the company sells. Identify the company's primary costs, and estimate the company's unit profit for that product or service. Conduct a break-even analysis if the company sold only that product or service. Write a paragraph about how varying parameters such as fixed costs, variable costs, and unit profit affect the break-even analysis.

Example: You could choose a gutter cleaning service. Fixed costs include equipment and trucks. Each gutter cleaning has a certain price to cover costs of labor and materials for that single cleaning.

Identify a business decision this company should consider. Decision tree and examine the situation. What would happen if the market gets stronger or weaker? Calculate expected returns from various possibilities. Determine the best course of action and write a paragraph explaining your reasoning.

Example: You could decision tree whether to invest in a better mower, in more advertising, or in a new employee. 

Project schedule for a business service or product. Identify the steps of the project and their dependencies. Estimate times and costs for those steps. Create a CPM/PERT network and find the critical path. Identify places where there is slack time. Which parts of the project may need to be crashed? How long is the project expected to take? Record your findings and write two paragraphs explaining your reasoning behind the schedule. Identify what you found out by doing your analyses.

Example: You could schedule for landscaping work on a customer's yard. Plans and drawings need to be made. Materials need to be purchased. Different parts of the yard may need to be dug up, while work can begin on others right away. But remember that you can't drive earthmoving machinery out over the finished product!


Identify a linear programming problem for your business. Set up an equation and a set of constraints and solve to determine the optimal solution. Write a paragraph discussing your solution method and what you found. Discuss how changes in the linear programming equation and constraints would change your solution.

Example: You could determine the optimal mix of lawn mowing and gutter cleaning tasks to fit your company's labor. Constraints would include the number of man-hours available, the number required for each task, and the numbers of tasks that are available to do any given week.

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