Alright, so i've been doing fairly well in Calculus so far this year, but for some reason optimization problems have been a bit over my head. Here's two that have been trouble for me:
1. Jasper has 100 ft. of fencing to construct a rectangular dog pen and he wants to maximize the area. let L be the length of the pen and W be the width.
a.) Write the formula for area in terms of L.
b.) Determine the dimensions of the pen that will maximize the area.
c.) Suppose there is already a wall in place for one side of the pen. If the same amount of fencing is to be used, what dimensions will maximize the area of the pen?
We're supposed to use the derivative to find the extreme value on both of these problems.
2. Jasper gets two dogs and decides the put a dividing fence in the middle of the rectangle. The fence along the outside of the pen is $4 /ft. but the dividing fence is $16 /ft.
a.) Jasper wants to spend $240 on fencing, so what is the maximum area he can enclose?
b.) If Jasper decides to enclose 300 sq. ft., what is the minimum cost?
Anyone care to help out a man in need?