### 4.5 Optimization II

**Optimization Word Problems**

In this section we are learning to apply our knowledge of optimization (section 4.4) in everyday life.

**Steps in solving an optimization word problem:**

1. Draw a picture.

2. Determine what you are maximizing and minimizing.

3. Find the constraints

4. Use constraints to rewrite the equation.

5. Find the derivative of the equation.

6. Find the zeros.

7. Test your answer to make sure it is correct.

**EXAMPLE PROBLEM:**

A father is planning to construct a large rectangular sand box for his kids. He has a total of 38 feet of wood to outline the edges of the box. Find the dimensions for the largest sand box he can create if he uses all of the wood.

**SOLUTION:**

**1. Draw a picture.**

**2. Determine what you are maximizing or minimizing.**

I am maximizing the Area.

**3-4. Find the constraints, and using constraints rewrite your equation.**

We only have 38 feet of wood available.

**5. Find the derivative of the new equation.**

**6. Find the zeros**

**7. Test it**

If the width is 9.5 and we have 2 widths and 2 lengths to add together than we can conclude that:

In conclusion: The dimensions of the rectangle, which actually seemed to be a square are

**9.5 feet by 9.5 feet.****ANSWER:**

9.5 feet by 9.5 feet

**OTHER SOURCES:**

This one is interesting. It has to do with optimization in marketing:

KATELYN!!!! you are up next. :)

If you are completely frustrated with these problems don't be worried. It takes practice, and I mean a lot of practice.

"It is not work that kills men, it is worry. Work is healthy; you can hardly put more on a man than he can bear. But worry is rust upon the blade. It is not movement that destroys the machinery, but friction."

-Henry Ward Beecher

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