# need help with Maximization

• Feb 25th 2010, 10:35 AM
Jlittl23
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?
• Feb 26th 2010, 04:46 AM
CaptainBlack
Quote:

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?

$X=100L - L^2$
$
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.