The utility function of a firm is given by U(q) = -2q2 + 40q + 12,580 (dollars). Determine the number of units that maximizes utility

1. Differentiate the utility function:

U(q) = -2q^2 + 40q + 12,580

U'(q) = \frac{d}{dq}(-2q^2 + 40q + 12,580) = -4q + 40

2. Set the derivative equal to zero to find the critical points:

-4q + 40 = 0

-4q = -40

q = 10

3. Use the second derivative to confirm it's a maximum:

U''(q) = \frac{d}{dq}(-4q + 40) = -4

Since U''(q) = -4 is negative, this confirms a maximum at q = 10.

Answer: The number of units that maximizes utility is q = 10 .