1 In a manufacturing company the production output P can be

1. In a manufacturing company, the production output P can be modelled using the function P(K, L) = c K0.4 L0.6 , where c is some constant, K is the input in capital, and L is the input in labour, all measured in some appropriate units. The present values of the variables are K = 160, L = 120, and P = 1400. How should the company management change the inputs in order to have a maximal increase in the output?

Solution

There seems to be something missing in the question. As per the given data (P=cK^0.4 L ^0.6), one may get the value of c by substituing K=160, L=120 and P=1400. This gives c=10.4 . However, in order to have maximal increase in output, there needs to some constraint on atleast on of the value else one may take any values of K and L.

Just try to run the following code in MATLAB

l=0:5:1000;
k=0:5:1000;
[X,Y]=meshgrid(x,y);

P=(X.^0.4).*(Y.^0.6);

surf(X,Y,P)
xlabel(\'K\')
ylabel(\'L\')
zlabel(\'P\')

and you will find that P is increasing function of L and K. Hence there is no end to increasing or optimizing the values as long as there is no other constraint.