Question

2.) What is the level of demand x or production that will yield the largest revenue? What level of demand x will yield the largest profit?

Answer 1

1. The vertex of the quadratic revenue function is halfway between the zeros.
R(x) = x(75 -3x) = 3x(25 -x) . . . . . has zeros at x=0, x=25

The level of demand that yields the largest revenue is x = 12.5.

2. Profit is the difference between revenue and cost.
P(x) = R(x) - C(x)
P(x) = -3x² +75x -125 -16x
P(x) = -3(x -59/6)² + 165 1/12 . . . . in vertex form

The level of demand that yields the largest profit is x ≈ 9.833.