Consider a price-taking firm whose production function is given by

q = 4 (L/5 + K/8)^1/2

whereL and K denote respectively the amount of labour and capital the firm uses to produce q units of output.

Suppose the price of labour is w = 17, the price of capital is r= 22 and the price of the firm's output is p=230 .

Determine the amount of capital the firm will use to minimize the cost of producing 1 unit of output at the input prices stated above.