A firm has the long-run cost function C(q)  7q2  175.In the long run, it will supply a positive amount of output, so long as the price is greater than

A) $70.
B) $148.
C) $35.
D) $140.
E) $75.

In the long run, a firm will supply a positive amount of output if the price is greater than the minimum average cost. The given cost function is $C(q)=7q^2+175$ . To find the minimum average cost, we first find the average cost (AC) function by dividing the total cost by q: $AC=\frac{7q^2+175}{q}=7q+\frac{175}{q}$ . To find the minimum of this function, we take its derivative with respect to q and set it equal to zero: $A{C}^{\prime }=7-\frac{175}{q^2}=0$ . Solving for q gives $q^2=\frac{175}{7}=25$ , so $q=5$ . Substituting q = 5 back into the AC function gives the minimum average cost: $A{C}_{min}=7(5)+\frac{175}{5}=35+35=70$ . Therefore, the firm will supply a positive amount of output as long as the price is greater than $70.