A competitive firm uses two inputs and has a production function f(x1, x2)  8x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1  w2  $1.The cost of producing y units of output for this firm is

A) 8(x1  x2) y.
B) 2(y/8) 2.
C) (x1  x2) /8.
D) y/16.
E) y₂/16.

The cost of producing y units of output is determined by the cost function, which in turn is derived from the production function and the prices of inputs. Given the production function $f(x_1,x_2)=8x_1^{0.25}{x}_2^{0.25}$ and the prices of both inputs being $1, the cost function can be found by solving for $x_1$ and $x_2$ that minimize the total cost subject to producing $y$ units of output. The correct answer, $2(y/8{)}^2$ , is derived by inverting the production function to solve for $x_1$ and $x_2$ as functions of $y$ , and then substituting these expressions into the total cost equation $w_1{x}_1+w_2{x}_2$ , given $w_1=w_2=1$ . This process involves using the properties of Cobb-Douglas production functions and their cost minimization conditions.