Optimizing:The Math that Saves

the World from Destruction

In understanding Optimization in Calculus, you will be able to save the

world from the ninja cows and from the evil robot dentists.

Promoting Black Bear Awareness

This Majestic Animal lives in 41 out of the 50 states. They all live on wildlife preserves, and they are known as the

“Defenders of Wildlife”.

Understand Optimization• In Optimizing problems, it usually consists of 2 variables, ‘x’ and ‘y’. Each

problem consists of 3 sides of a square and you have to find the length each side has to be. To help with this, you are usually given the total length of the entire fence. You use to this find the maximum area possible.

• For example, if you have 500 yards of fencing, and you want to fence in an area with a building next to it. So you have these 2 equations:

X+2Y=500, and Area=XYSet X = 500 – 2Y and plug that into your Area equation, and you should get

Area = Y(500-2y) = 500Y-2Y2.Having this, you take the derivative, and you’ll get

0 = 500 – 4Y, then find Y500 = 4Y, You find Y = 125

The reason you take the derivative is so you can find the critical point.Since you have Y now, you can plug in that number the equation: X + 2Y =

500.X + 2(125) = 500X = 250Finally, you found both lengths in order to find the maximum area possible.

Are You Tired of the Everyday Apple? Try something new!

Exotic Fruits such as shown below are exciting, fresh, and uncannily healthy. Eating these as you progress through this helpful guide will increase

your learning capabilities and understanding.

Robot DentistsThere are over 40,000 robot dentists in the world, and in order to keep them from

operating on the world, we must capture them. One wall is a highly magnet sensitive to certain parts of the robot, but this is not enough to hold them there for long. We need more of this fencing on the other three sides to keep them locked in place. Each robot dentist take up an area of two feet. So, the Area needed to hold them is 80,000 feet (they don’t need room because they are robots). So we use the Optimizing Equation and find that 2X + Y = ?? And XY = 80,000.

So, we cant set Y = 80000/X and plug that into the equation 2x+Y = ?. You will get: 2X + (80000/X). You take the Derivative of the function and find 2 + 80000/X2 = 0. Now you solve for X.

2 = 80000/X2, 2x2 = 80000. They both have to be positive, because Area is always positive. You find X = 200, and knowing this, you can plug it into your Area Equation.

XY = 80,000, 200Y = 80,000. Y = 400.Knowing this, you now have the perimeter u need, which is 800.

Fun Intermission

Although Martin hates this horse, it still loves

him, kinda like he hates Jeebus, yet Jeebus loves

Him.

Ninja Cows• These nasty buggers are the more dangerous than the robot dentists. There are approximately over 100,000

ninja cows. Each cow is 5 feet high and 4 feet wide. Luckily, we have 500,000 feet of electric fence, but we are uncertain if this will be enough to contain them, because they can hop over the fence, unlike their robot dentist counterparts. So to counteract this problem, we will first find the area needed to box them in, and later, we will find the surface area needed for the roof.

• First, we know that XY = 400,000 and 2X + Y = 500,000. For now, let us pretend that we do not know the area, and doing this, find Y. 2X + Y = 500,000, so Y = 500,000 – 2X. Knowing this, plug this into the area equation (XY = Area). X(500,000-2X) = Area. When we take the derivative, we get 500,000 – 4X = 0. X = 125,000. Having X, plug this into the Perimeter equation (2X + Y = 500,000). 2(125,000) + Y = 500,000. We find Y = 250,000. So yes, we have enough material to box the Ninja Cows. So, lets find the perimeter for this box using as little as possible.

• Lets go back and find Y using the Area equation. You find Y = 400,000/X. Now, we plug this into the perimeter equation. 2X + 400,000/X = P. Take the derivative. 2 - 400,000/X2 = 0. You find X = 447.2135955. Now, plug this into your Area equation. 447.2135955Y = 400,000. Y = 894.427191. We have used up 1,788.854382, but lets just say 1,800.

• RECALL: We still need to find the top of the box. This isn’t hard, because all you need is to find the area, which is simply find the area, Length x Width. The length is Y and the width is X.

• Just Multiply 447.2135955 x 894.427191 = 400,000.• SUCCESS!!! We have just enough electric fencing to ensnare all the ninja cows.

• Congrats

A Enlightening IntermissionIf you are depressed, such as Martini Quincy Bakehead (not Martin Baker), you may have

these symptoms:• Constant sadness • Irritability • Hopelessness • Trouble sleeping • Low energy or fatigue • Feeling worthless or guilty for no reason • Significant weight change • Difficulty concentrating • Loss of interest in favorite activities• Maybe a bit OgreishBut, there is hope for you yet by calling 1-800-273-TALK. They can help you get over your

life and make sure you don’t kill yourself. Kinda like Martini’s dog which hanged itself out of desperation from its beating.

The World is Saved

• Thankfully you saved the world, but due to the environmental concerns for some much electrical fencing, the environmentalists of the world have united against you and brought you to justice. Before you were sent to jail, you managed to abrakabra you way out of the transport vehicle. The secret to your trick was a saw and a table. How lucky is that? Having a saw in there with you,

its like someone planted it there for you to escape.

And yesI am a Serious Guy, kinda like this Cat