Economics question; Help me!!?

Question

I was wondering if someone could show me a walk through of this one. Thank you!

A competitive firm has a production function of the form Y=2L + 5K. If W= $2 and r=$3, what will be the minimum cost of producing 1 units of output?

Please show me how you reached your conclusion because I'm a little confused on how to tackle this. thanks!!

Answer 1

It would help if you said what the letters mean. What is "K"? What are the others?

Answer 2

TC=wL+rK = 2L+3K

Equilibrium:

MPL/w=MPK/r

MPL=(Y)'=2

MPK=(Y)'=5

MPL/2=2/2

MPK/3=5/3

Since 5/3 is highest value - thus capital gives higher product per dollar spent - so producer should choose only capital in production and no labor at all

L=0

Y=10

10=2L+5K = 5K

K=10/5=2

TC=2*0 + 3*2=6

Minimum TC(Y=10) = 6$