Calculus Optimization Word Prob

Hi, I have 2 questions on these words problems. I really am not sure where to start these.

1. An advertisement consists of a rectangular printed region with margins of 2 inches each at the top and bottom and 1 inch at each side. If the area of the printed region is to be 98 in^2 , find the overall dimensions if the total area of the advertisement is to be a minimum.

2. A rancher is going to build a 3-sided enclosure with a divider down the middle. The cost per foot of the 3 side walls are $6/ft, with the single back wall being $10/ft. The area enclosed will be 180 ft^2. What dimensions would minimize the cost?

The pen looks like this.

____

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for this one I had an idea of setting 180ft^2 = 3y+x but am not sure if this is the right way to start.

Pay attention to square root

Quote:

Originally Posted by

**drewms64** Thanks for the advice on both of the questions, for this one would it then end up being,

x=b y=l

$\displaystyle

A(y)= \left(\frac{98}{y-4}+2 \right)y

$

$\displaystyle

= \left(\frac{98y}{y-4}+2y \right)

$

$\displaystyle

A'(y)= \left(\frac{(y-4)(98)-(98y)(1)}{(y-4)^2)}+2 \right)

$

$\displaystyle

= \left(\frac{-392}{(y-4)^2}+2 \right) = 0

$

not sure how to get [tex] to work for this one, but

-392(y-4)^-2 = -2

(y-4)^-2 = 196

take the -2 root of each side

y-4 = - 14

y = -10

then when I find x I get -5

I dont think these should be negative though?

There is not such thing as -2 root. You should apply the cross product rule:a/b=c/d is equivalent to a*d=b*c.

therefore, (y-4)^-2=196 becomes (y-4)^2=1/196 and now apply the square root to find

y-4=1/14 or -1/14

So, your solutions are y=4+1/14 and y=4-1/14, both positive.