Question

A rectangular field is to be enclosed on four sides with a fence. Fencing costs ​$4 per foot for two opposite​ sides, and ​$3 per foot for the other two sides. Find the dimensions of the field of area 650ft2 that would be the cheapest to enclose.

Answer 1

Explanation:

Lets suppose the one side be x and the other side of the rectangle be y

given area
`x*y=650ft^2`

implies x = 650/y

Cost = 2*4*x+2*3*y=8x+6y

= 8*650/y + 6y

= 5200/y + 6y

upon differentiating we get

=
`-5200/y^2 + 6=0`

`y^2`= 2600/3

y=
`10√(26/3)`= 43.3

x= 15

C(43.3)=
`10400/(43.3)^3`>0 hence it is a minima value

optimizing the result we get

Cost = 8*15+6*43.3 =$ 379.8