Question

What output will maximize total revenue if TR = 250q − 2q^2

Answer 1

or if you are not into calculus
find the vertex of the parabola halfway between zeros
0 =( 250 - 2 q) q
zeros at q = 0 and q = 125
half of 125 = 62.5

Answer 2

To find the output that maximizes total revenue, we need to find the derivative of the total revenue function with respect to q and set it equal to zero.

The total revenue function is TR = 250q - 2q^2.

Taking the derivative of TR with respect to q, d(TR)/dq, we get:
d(TR)/dq = 250 - 4q

Setting this equal to zero:
250 - 4q = 0

Solving for q:
4q = 250
q = 62.5

Therefore, the output that maximizes total revenue is q = 62.5.

Answer 3

Apologies for the confusion. Yes, another way to find the output that maximizes total revenue is by finding the vertex of the parabola formed by the total revenue function.

The total revenue function is TR = 250q - 2q^2.

To find the vertex, we can use the midpoint between the two zeros of the function. The zeros of the function occur when TR = 0, so we have:
0 = (250 - 2q)q

Setting each factor equal to zero:
250 - 2q = 0 --> q = 125
q = 0

The zeros of the function are at q = 0 and q = 125. The midpoint between these zeros is:
(q1 + q2)/2 = (0 + 125)/2 = 62.5

Therefore, the output that maximizes total revenue is q = 62.5.