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Q=K^a L^b cobb douglas production function
a+b=1 , a=b elasticity is same and equal to1
P=P' Constant price because of perfect competition
C=wL+rK Cost Function
R=Q*P Revenue function
PI=R-C Profit function
use given data to find level of L,K where profit is maximum?
Thanks for the invite, I apologize for the answer, I leave the answer for the professionals
Thank you for inviting me to answer, but I have no experience in mathematical economics.