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# Finding optimal combination of inputs

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Let the production function be given by
Q = K^1/2*L^1/2, WL=\$5, WK=\$20,

Suppose the plant size (K) is fixed in the short run at 100.

A. With K = 100, how many units of L are required to produce 400 units of
output?
a. 400
b. 100
c. 1600
d. 3200
e. none of the above

B. If this amount of labor (found in question A) is combined with 100 units of K:
a. MPL/WL = MPK/WK
b. MPL/WL > MPK/WK
c. MRS = WL/WK
d. MPK/WK > MPL/WL
e. Two of the above.

https://brainmass.com/economics/production-function/finding-optimal-combination-inputs-356717

#### Solution Preview

A. With K = 100, how many units of L are required to produce 400 units of
output?
a. 400
b. 100
c. 1600
d. 3200
e. none of the above

Q = K^1/2L^1/2
Marginal Product of capital=MPK=dQ/dK=1/2*K^(-1/2)*L^1/2=0.5K^(-0.5)L^0.5
Marginal ...

#### Solution Summary

Solution describes the steps to find the optimal combination of two inputs with the help of information provided.

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