question a rectangular plot of land requires fencing on all 4 sides. two opposite sides will use heavy duty fencing at £6/metre, whilst the other tow sides will use standard fencing at £3/metre. if the farmer buying the fencing has £5000 to spend, what is the maximum area he can enclose? attempt let y = heavy duty fencing sides and x= standard fencing sides. A=x*y 5000=6y+6y+3x+3x 5000=12y+6x...solve for x (or y)... 5000-12y=6x (divide by 6)... 833.33-2y=x....Now we will substitute this in to A=x*y A=(833.33-2y)*y A=833.33y-2y2 ....now take derivative and set equal to 0 A'=833.33-4y=0 or...4y=833.33 y=208.33 meters.find x 5000-(12*208.33)=6x 2500=6x x=416.66 meters So max area is x*y or (208.33*416.66)= 86803m2.