Problema Solution
A rectangular field will be fenced on all four sides. Fencing for the north and south sides costs $9 per foot and fencing for the other two sides costs $8 per foot. What is the maximum area that can be enclosed for $4800?
Answer provided by our tutors
let
l = the length of the field that is the length of the north = the length of the south side
w = the width of the field that is the length of each of the other two sides
9(2l) + 8(2w) = 4800 divide both sides by 2
9l + 8w = 2400
w = (2400 - 9l)/8
w = 300 - (9/8)l
the area of the field is
A = l*w
A = l*(300 - (9l)/8)
A = 300l - (9/8)*(l^2) is a parabolic function with quotient -9/8 <0 in front of l^2 thus the function has maximum equal to it vertex
c - b^2/4a, where a = -9/8, b = 300, c = 0
0 - (300^2)/(4*(-9/8)) = 20,000 ft^2
the maximum area that can be enclosed is 20,000 ft^2.