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Chapter 5: Problem 28

Describe a situation in your life in which you would really like to maximize something, but you are limited by at least two constraints. Can linear programming be used in this situation? Explain your answer.

Short Answer

Expert verified
Yes, linear programming can be used in a scenario where you want to maximize the number of books read in a year, which is limited by time and money constraints. It helps to make an optimal decision by finding the best way to allocate scarce resources.

Step by step solution

01

Identify a Situation

Think of a situation where you have a clear objective that you would like to maximize. For example, let's say you want to maximize the number of books you read in a year.
02

Identify the Constraints

Pinpoint what restrictions are limiting your goal. In this example, constraints could be time (only so many hours to read in a day) and money (limited budget to buy new books).
03

Applying Linear Programming

Linear programming could be used here to optimize your goal given the constraints. For example, to maximize the number of books read, you could allocate specific hours of the day for reading (time constraint) and make a budget for buying new books (money constraint). The value to be optimized (number of books read) would be a linear function of the variables (time and money), and the constraints would form a feasible region within which the solution lies.
04

Explain the Application of Linear Programming

State why linear programming is effective in this situation. In our example, linear programming helps to achieve the maximum number of books read under given constraints. It assists in making an optimal decision by finding the best way to allocate scarce resources.

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Most popular questions from this chapter

write the partial fraction decomposition of each rational expression. $$ \frac{3 x^{3}-6 x^{2}+7 x-2}{\left(x^{2}-2 x+2\right)^{2}} $$

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Because \(x+5\) is linear and \(x^{2}-3 x+2\) is quadratic, I set up the following partial fraction decomposition: $$ \frac{7 x^{2}+9 x+3}{(x+5)\left(x^{2}-3 x+2\right)}=\frac{A}{x+5}+\frac{B x+C}{x^{2}-3 x+2} $$ Because \(x+5\) is linear and \(x^{2}-3 x+2\) is quadratic, I set up the following partial fraction decomposition: $$ \frac{7 x^{2}+9 x+3}{(x+5)\left(x^{2}-3 x+2\right)}=\frac{A}{x+5}+\frac{B x+C}{x^{2}-3 x+2} $$

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