Your dream of becoming a hamster breeder has finally come tr

Your dream of becoming a hamster breeder has finally come true! You are constructing a set of rectangular pens in which to breed your furry friends. The overall area you are working with is 144 ft^2 and you want to divide the area up into six pens of equal size as shown below. The cost of the outside fencing is $10/foot. The inside fencing costs $5/foot. Find the dimensions of each pen that will minimize the cost. What is the total cost? \"Ninety percent of hockey is mental the

Solution

let x be the width of each individual pen and y be the length since the total area is 144 ft^2 each individual pen will have an area of 24square feet

there is 5y feet of interior fencing

xy=24

y=24/x

2y+12x for exterior fencing

since the total cost C=5(5y)+10(2y+12x)=45y+120x

C=45(24)/x+120x

C\'=-1080/x^2+120

which implies x== or -3

let us take x=3

y=24/x=24/3=8

so C=45y+120x=45(8)+120(3)=720