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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 6.2, Problem 1E

Textbook Problem

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Exercises 1-24, solve the given LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. [**HINT:** See Example 1.]

Maximize

Subject to

To determine

**To calculate:** The optimal solution of given linear programming problem to maximize

**Given Information:**

Maximize

**Formula used:**

Following the steps to find the optimal solution of linear programming problem:

1) Draw a rectangle large enough that all the corner points are inside the rectangle.

2) Shade the outside of the rectangle so as to define a new bounded feasible region and locate the new corner points.

3) Obtain the optimal solutions using bounded feasible region.

4) If the optimal solution occurs at the one of the corner points, then LP problem has that corner point as optimal solution otherwise it has no optimal solution.

**Calculation:**

Consider the first constraint equation,

Isolate the variable *y*, by subtracting

Isolate the variable *y*, by dividing

To plot the graph of the function, find the ordered pairs of the equation by substituting different values of *x*.

For *x*,

For *x*,

For *x*,

Construct a table for the ordered pairs,

x |
0 | 1 | 3 |

y |
4.5 | 4 | 3 |

Test the first inequality by

The inequality is satisfied. If the test point satisfies the inequality then the set of solutions is the line plus the entire region on the same side of the line as the test coordinate

Consider the second constraint equation.

Isolate the variable *y*, by subtracting

To plot the graph of the function, find the ordered pairs of the second constraint equation by substituting different values of *x*.

For *x*,

For *x*,

For *x*,

Construct a table for the ordered pairs of second constraint equation,

x |
0 | 1 | 2 |

y |
9 | 7 | 5 |

Test the second inequality by (0,0) test coordinates

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Study Guide for Stewart's Multivariable Calculus, 8th

What is the expected value of a random variable? Give an example.

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In Exercise 9 to 16, use a calculator to find the indicated cosine ratio to four decimal places. cos0

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Describe the pattern that would appear in a scatter plot showing the data points for each of the following corr...

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Express each percent as a decimal fraction or mixed decimal. 38. 0.6%

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Perform each operation and write each complex number in a+bi form. (3+5i)+(43i)

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A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x i...

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In August 2009, Harris Interactive released the results of the Great Schools survey. In this survey, 1086 paren...

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In Exercises 23-32, write an expression for the nth term of the geometric sequence. Then find the missing term....

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Write the first four terms of the sequences defined by the formulas in 1-6. dm=1+(12)m for every integer m0.

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