A firm has the short-run total cost function c(y)  9y2  144.At what quantity of output is short-run average cost minimized?

A) 4
B) 16
C) 0.75
D) 3
E) None of the above.

To minimize the short-run average cost (SAC), we first need to find the SAC function by dividing the total cost function by the quantity of output (y). The given total cost function is $c(y)=9y^2+144$ . The SAC is then $SAC=\frac{9y^2+144}{y}$ .To find the minimum, we take the derivative of the SAC with respect to y and set it to zero. The derivative of SAC with respect to y is $SA{C}^{\prime }=\frac{d}{dy}(\frac{9y^2+144}{y})=18y-144/y^2$ .Setting $SA{C}^{\prime }=0$ gives $18y-144/y^2=0$ . Solving for y, we find $y=4$ , which is when the short-run average cost is minimized.