2. A plant's production function is Q = 2LK-K 2 , where Q is its output, L is the amount of labour

and K is the amount of capital. In the long run, the plant chooses the optimal proportion of labour

and capital. The price of labour is $2 per unit and the price of capital is $1 per unit. In order to

produce 8 units of goods, what are the optimal amounts of K and L?