isocost/isoquant economics problem
Hi all, I've become really stumped on this problem. I'm starting to think the information given in the problem is wrong. Anyways, this is what I have.
Q=150K^.75L^.25 where Q=2500
TC = 5.50K + 8.50L
w (wage rate)=8.50
r (capital rate)=5.50
Slope of isocost line = w/r = 8.50/5.50 = 1.55
Slope of isoquant = mrts = .25K/.75L which reduces down to .33K/L
Set the two slopes equal so 1.55=.33K/L
1.55L=.33K, solve for L so L=.21K
Now at this point, I believe everything I have done is right because it's not hard calculations.
Plug that L=.21K into the original function so, 2500= (150K^.75)(.21K^.25), which reduces to 2500=31.5K and K=79.37
Multiply 79.37 by .21 to get L and I got L=16.67.
I don't think my math is wrong there but it could be. But when you put 79.37 and 16.67 back in for K and L in the original function, the output is somewhere around 8000 which is clearly not 2500. Is there anything anyone may see that I could have messed up on? Thank you for any help!