Question

A rectangular area of 2,000 square feet is to be fenced on three sides with fence costing $0.30 per foot and on the fourth side with fence costing $0.50 per foot. If x denotes the length of the fourth side and C = ƒ( x ) denotes the corresponding cost of the fence in dollars. Express C as a function of x .

Answer 1

f(x) = 0.80x +
`(1200)/(x)`

Explanation:

Let a rectangular area is having two sides = x foot and other two sides measure = y foot

As per the statement given in the question, if C is the cost to fence three sides (two sides with y foot and one side with measure x)

C = f(x) = 0.30(2y+x) + 0.50(x)

C = 0.60y + 0.30x + 0.50x

C = 0.80x + 0.60y

We know area of a rectangle is represented by

A = xy

2000 = xy

`y=(2000)/(x)`

Now we replace the value of y in equation 1

C =
`f(x)=0.80x+0.60((2000)/(x))`

f(x) = 0.80x +
`(1200)/(x)`

Therefore, the cost to fence the rectangular area can be represented by

C = f(x) = 0.80x +
`(1200)/(x)`