A farmer wants to fence in a rectangular field that encloses 3600 square feet. One side of the field is along a river and does not require fencing. The fencing costs $3.50 per foot. Express the total cost C(x) of the fencing (in dollars) as a function of x.

Accepted Solution

Answer:C(x) = [tex]\$3.50(\frac{x^2+7200}{x})[/tex]Step-by-step explanation:Data provided in the question:Area of the field = 3600 square feetFencing charges = $3.50 per footLet the side along the river be 'x' feet and the other side of the 'B'now,Area of rectangle = Bx = 3600 square feetorB = [tex]\frac{3600}{x}[/tex] feetand total length to be fenced = x + 2Btherefore, Total cost of fencing = Fencing charges Γ— total length to be fencedorTotal cost of fencing = $3.50 Γ— ( x + 2B )substituting the value of B from (1)Total cost of fencing, C(x) = [tex]\$3.50(x+2\times\frac{3600}{x})[/tex]orC(x) = [tex]\$3.50(\frac{x^2+7200}{x})[/tex]