Calculus Help!!

Question

A farmer wants to fence in a rectangular field. The farmer must use a different type of fencing for each pair of parallel sides of the field. One type costs $10 per metre, and the other type costs $5 per metre. Assuming the farmer can spend $800 on fencing in total, what are the dimensions of the largest possible field she could make?

Answer 1

40 m of cheaper fencing for 2 parallel sides

20 m of the more expensive for the other 2 parallel sides

for a max are = 40x20 = 800 square meters

Answer 2

L:et dimentions is x by y. Then area A = xy and 20x + 10y = 800; y = 80 - 2x,

A = x(80 - 2x) = 80x - 2x²; dA/dx = 80 - 4x = 0; x = 20; A'' = - 4 < 0. So we have maximum area

x = 20 m; y = 80 - 40 = 40 m