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

Answer:

Step-by-step 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= $10\sqrt{26/3}$= 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