A farmer wished to fence in a field with an area of 1850 ft2

A farmer wished to fence in a field with an area of 1850 ft^2 with a fence in the middle dividing the field into two areas. He then wants to put in a gate on one side of the field, and another gale in the middle fence with each gate having a width of g = 8 ft. (a) Express the length I of the field as a function of the width omega l(w) = 1850/w (b) If the fencing costs $10 per foot, express the cost of the fencing C as a function of the width omega. Do not include the lengths of the gates. C(w) = (30 (w))+37000/w

Solution

a)

area =l*w =1850

=>l=1850_/w

length of field l as function of width w is l(w)=1850/w

b)

cost,C(l,w)=10*(l+l+(w-8)+(w-8)+w)

cost,C(l,w)=10*(2l+3w-16)

cost,C(w) =10*((2*1850_/w)+3w-16)

cost,C(w) =10*((3700_/w)+3w-16)

cost,C(w) =((37000_/w)+30w -160)