Question

Supposed that a firm's daily output is
Q = 1.5L^0.76 K^0.24
Q = Daily output
L = number of workers
K = number of machines used per day
Price per output = $10

If wages of a worker is $30 a day, how many workers(L) per unit of output should the firm hire?

Here's what I did, to optimize cost, we use the equation marginal price for workers = marginal price for machines
MPL/PL = MPK/PK.
MPL = dQ/dL = 1.14(K/L)^0.24
MPK = dQ/dK = 0.36(L/K)^0.76 = 0.36(K/L)^(-0.76)

MPL/MPK = PL/PK = 1.14K/0.36L = 30/PK
Now here's where I'm stuck. What can i do to $10 per unit of output to answer the question? Do I even need that?