A firm's technology requires it to combine 4 labor hours with 3 machine hours to produce 1 unit of output. So capital and labor are perfect complements. So the production function is f(E, K) = min(E/4, K/3). The firm wants to produce q units of output, where q > 0 is some number. Suppose the price of capital is $10 per machine per hour. What combination of inputs will the firm use if the wage rate is $10 per hour? What combination of inputs will the firm use if the wage rate is $15 per hour? What if one of the inputs (but not both) is free?