[avenger9000]

Ok I am stuck on this I have tried to do it but am stuck

A firm has production function Q = (L^0.5 + K^0.5)^2



if it wishes to produce 121,000 units of output, find the cost minimising combination of labour and capital. The price of Labour is 10 and the price of capital is 1

Here's what I have done so far:


The cost minimising condition occurs where the marginal rate of technical substitution equals the ratio of the prices of inputs

so:

Q = L + 2(KL)^0.5 + K

Marginal product of Labour = 1 + (K/L)^0.5
Marginal product of Capital = 1 + (L/K)^0.5

so

1 +(K/L)^0.5 / 1 + (L/K)^0.5 = 10

and I am stuck here not sure what to do next can anyone point me in the right direction thanks