Please help. Thanks.?
To maximize output given the production function and constraint below, please help me find the optimal level of labor. The production function is defined as: Max Q = 6K + 20L – 0.025K² – 0.05L², subject to the constraint 3K + 8L = 1140.
What is the level of labor (L) that maximizes output?
A. 283.13
B. 292.31
C. 198.32
D. 189.23
Thank you!
1 Answers
Rearrange the constraint:
K = (1140 – 8L) / 3
and plug it into the quantity function:
Q = 6(1140 – 8L)/3 + 20L – 0.025[(1140 – 8L)/3]² – 0.05L²
which simplfies to
Q = -0.227778L² + 54.6667L – 1330
Take the derivative w/r/t L to maximize Q:
dQ/dL = 0 = -0.45556L + 54.667
L = 120
I don’t get any of your answers.
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