Linear Relationships

Question

Linear relationships between two quantities can be described by an equation. The purpose of this assignment is for you to identify, interpret and evaluate the use of an equation in a real world situation.
– Using an online source, such as online news magazine, online newspaper, or Google search engine, find an article that uses a linear equation in a real world situation.
– Cite the source from which you took the equation.
– In 2-3 paragraphs with a minimum of 5 sentences each, write a descriptive essay. In your essay, describe the context in which the equation is used, describe the meaning of your equation which must include the meaning of each variable. Explain what is meant by the solution to the equation. In your opinion, does the source evaluate the equation in a manner acceptable to you? Why or why not? Explain your reasoning.

Question

Use simultaneous equations to determine the optimal values of the decisions variables. I am also asked to show GRAPHS and explain my work.
 

Maximize Z=6A+3B(revenue)

Subject to

Material 20A+6B<=600lb

Machinery25A+20B<=1,000hr

Labor 20A+30B<=1,200hr

A,B>=0

1. What are the optimal values of the decision variables and Z?

2. Do any constraints have (nonzero) slack? If yes, which ones and how much slack does each have?

3. Do any constraints have (nonzero) surplus? If yes which ones and how much surplus does each have?

4. Are any constraints redundant? If yes, which ones? Explain briefly.