Thread: Optimal production?

I need to find the optimal level of inputs, the minimum total cost, and the average cost given the following conditions:

Min 25K + 5L
s.t.

The second equation looks like a standard Cobb-Douglas production function, but I don't understand how they interact.

Originally Posted by Quixotic

I need to find the optimal level of inputs, the minimum total cost, and the average cost given the following conditions:

Min 25K + 5L
s.t.

The second equation looks like a standard Cobb-Douglas production function, but I don't understand how they interact.

The constraint condition is:



raise this to the fourth power:



so



Substituting this into the objective gives:



Now the minimum of the objective occurs when:



etc.

CB