Question
The utility function of a firm is given by U(q) = -2q2 + 40q + 12,580 (dollars). Determine the number of units that maximizes utility
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Answer to a math question The utility function of a firm is given by U(q) = -2q2 + 40q + 12,580 (dollars). Determine the number of units that maximizes utility
Sigrid
4.5120 Answers
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 isq = 10
2. Set the derivative equal to zero to find the critical points:
3. Use the second derivative to confirm it's a maximum:
Since U''(q) = -4 is negative, this confirms a maximum at q = 10.
Answer: The number of units that maximizes utility is
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