Try finding the area in terms of the width and the length (the diagram below may help with this) and then finding the length in terms of x so you can substitute it in.1. A rancher has 360 yards of fencing with which to enclose two adjacent rectangular corrals, one for sheep and one for cattle. A river forms one side of the corrals. Suppose the width of each corral is x yards.
a) express the total area of the two corrals as a function of x.
obviously, the width can't be negative or the sheeps and cows will fall in the river. You also need to be sure that the length isn't negative either.b) find the domain of the function
First get the area of each of the sides in terms of x and the height, then find the height in terms of x and sub it in. from there you can easily get the cost.2. A rectangular box with volume 320 cubic feet is built with a square base & top. The cost is $1.50/square foot for the bottom, $2.50/square foot for the sides, and $1/square foot for the top. Let x=the length of the base, in feet.
a) Express the cost of the box as a function of x.
The domain can be found in a similar manner to the last question.
Check stationary points (where the derivative is 0) and endpoints and take the smallest cost. Then find the height for that width.c) what dimensions minimize the cost of the box?