12.2 Pre Calc Homework

Question

For tax reasons, I need to create a rectangular vegetable patch with an area of exactly 32 square feet. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. What are the dimensions of the vegetable patch with the least expensive fence?

north and south sides ____ ft

east and west sides ____ ft

Answer 1

Hi,

a = length b is width area = ab = 32

cost for east and west = 2b(4)

cost of north and sought = 2a(2)

cost = y = 8b + 4a Now find a or b of given information ( area)

I found a = 32/b then plug in to the function ( cost)

y = 8b + 4a = 8b + 4 ( 32/b)

y' = 8 - 128/b² then y' = 0 ------> 8 = 128/b² ------> b = 4 ( east) then

find a = 8 north

I hope it is useful,

Minoo