A factory that you are managing has an hourly production process that can be represented by the following Cobb Douglas Production function: Q = 20K^0.5L^0.50

The price of one unit of capital per hour is $30 or r =30 and the price of one unit of labour per hour is $10 or w = 10. Your total cost should not exceed $1,000. Thus,

TC = 1,000. Find the optimal amount of labour and capital that you will be using, and compute the total amount of Q. Include a diagram