# Math Help - need help with Maximization

1. ## need help with Maximization

2. Suppose a company produces a commodity X using an input L. The production function is X =
100L – L2.
(a.) Find what level of L maximizes production output, X.
(b.) What levels of L generate an output of X = 0? (there are two different L values)
(c.) Plot the production function
(d.) Find the marginal product of labor (MPL).
MPL=100-2L
(e.) For what values of L is the MPL increasing and decreasing?

2. Originally Posted by Jlittl23
2. Suppose a company produces a commodity X using an input L. The production function is X =
100L – L2.
(a.) Find what level of L maximizes production output, X.
(b.) What levels of L generate an output of X = 0? (there are two different L values)
(c.) Plot the production function
(d.) Find the marginal product of labor (MPL).
MPL=100-2L
(e.) For what values of L is the MPL increasing and decreasing?
Your production function is:

$X=100L - L^2$

Now as you have posted to the calculus forum you will have been taught that a maximum if one exists will be a root of:

$
\frac{dX}{dL}=0
$

So for part (a) you must differentiate $X$ with respect to $L$ set the derivative to zero and solve for $L$. Then you will need to check that this is indeed a maximum.

CB