zombie cancer a cozy riverside village, psychotropic town, is about to be quarantined because of a...
TRANSCRIPT
Zombie CancerA cozy riverside village, Psychotropic Town, is about to be quarantined because of a
deadly outbreak of an unnamed virus. The virus is Angry Duck Eating Soap (ADES). In
order to protect the neighboring village, you will need to construct a fence around this town. Of course, because the mayor
of Psychotropic Town is a money grubbing cretin, he wants you to construct it with
1000 feet of fence and create the largest area possible. Since a river borders one
side of the town, you won't need to fence that side off. People with ADES can't
swim... duh...
Variable & Equation Declaration
x = lengthy = width
A = xy (Primary)2x + y = 1000 (Secondary)
Solving for width(y)
2x + y = 1000y = -2x+1000
Creating a New Area Equation
A = (x)(1000-2x)A = 1000x – 2x22
Differentiating the Area Equation
A = 1000x – 2x22
A' = 1000 – 4x
0 = 1000 – 4x-1000 = -4x
X = 250
0Length is 250 feet.
Solving for width
1000 = 2x + y1000 = 2(250) + y
1000 = 500 + y500 = y
Width is 500 feet.
Proving ourselves
Second Derivative TestA'' = -4
(it is concave down, meaning it's a relative maximum)
Happy F-Bomb FactoryHappy F-Bomb factory is making a new
product, the 7-Bomb. In order for the shipping to commence, an appropriate and
environment-friendly cost plan has to be mapped out. Determine the production level that will maximize the profit for the company
with cost and demand functions: C(x)=84+1.26x-0.01x2+0.00007x3 and
p(x)=3.5-0.01x and what is the maximum profit?
Variable and Equation Declaration
x = units P = profit (R – C)p(x) = 3.5 - .01x
C = C(x) = 84+1.26x-.01x2-.00007x3
R = p(x)[x] = 3.5x-.01x2
Solving for Profit
P = R – CP = 3.5x – 0.01x2 – 84 – 1.26x + 0.01x2 –
0.00007x3
= -0.00007x3 + 2.24x - 84
Solve for x!
P' = -0.00021x2 + 2.24x2 = 10666.666
X = 103.28
We should create 103.28 7-bombs
Insert x into equation
P(x) = -0.00007x3 + 2.24x -84P(103.28) = 70.23
$70.23 is our maximum profit
Proof of PURCHASE !$#@
P''(x) = -.00042xP''(103.28) = -0.0433776
Negative = Maximum = Concave Up = Yeah
☺Conclusion☻
Using derivatives allow you to find great deals on products, and how much (or little) of stuff
you have to do for the most (or little) of something else!
It also allows Mrs. Lustgraaf to derive the maximum possible grade for this
presentation!!