Please help. Thanks.?

Find the level of labour that will maximize Output given the production function and constraint below:

Max Q = 6K + 20L – 0.025 K² – 0.05 L²;

subject to 3K + 8L= 1140 

A. 283.13

B. 292.31

C. 198.32

D. 189.23

1 Answer

  • 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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