Q=10L^0.25 K^0.75L=20K=30Q=16001) WHAT IS THE OPTIMAL COMBINATION OF INPUT?2) BASED ON THIS ANSWER...

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Q=10L^0.25 K^0.75L=20K=30Q=16001) WHAT IS THE OPTIMAL COMBINATION OF INPUT?2) BASED ON THIS ANSWER BASED ON A BUDGET OF $4,000 WHAT IS THE MAX OUTPUT PRODUCE?

David · Accepted Answer

Answer to 1: 
Q = 10*L^(0.25)*R^(0.75)  
Price of Labor = $20 and price of raw material (R) = $40 
The company wants to produce 1600 units of output. 
Marginal product of labor (MPL)= dQ/dL = 10*0.25*[(R/L)^(0.75)] 
Marginal product of Resource (MPR) = dQ/dR = 10*0.75*[(L/R)^(0.25)] 
So MPL/MPR = R/3L 
price of labor/price of resource = 20/40 =1/2 
At optimum,

Q=10L^0.25 K^0.75L=20K=30Q=16001) WHAT IS THE OPTIMAL COMBINATION OF INPUT?2) BASED ON THIS ANSWER BASED ON A BUDGET OF $4,000 WHAT IS THE MAX OUTPUT PRODUCE?

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