farmer wishes to fence a rectangular area along the river bank. No fence is required on the side adjacent to the river. The material for the fence costs P16.00 per meter for the side parallel to the river, P12.00 per meter for the side perpendicular to the river. The farmer has a budget of P12 000.00. Find the dimension of the lot that will have the largest possible area.

? :O i'm not sure how to solve this. :(

3 answers

Assuming farmer uses up his budger of 12000, and let
L=length along river (costs 16/m)
w=width (costs 12/m)
L=(12000-12w*2)/16
Area,
A(w)=w(12000-24w)/16
=750w-(3/2)w²
Differentiate with respect to w and equate to zero for maximum:
A'(w)=750-3w=0
w=250
L=(12000-24w)/16=375

2+2= fish right?

L= 60m
W= 30m