Miguel and Jake run a paper company. Each week they have a $12,000 to spend on producing reams of paper. The paper plant's long-run production function is = ^1/32/3, where Q is the number of paper reams produced, K is the quantity of the capital rented, and L is the quantity of labor hired. For this production function, the = 2^1/3/3^1/3 and the = ^2/3/3^2/3. The rental rate for capital is $30, and the wage rate is $40. a. What ratio of capital to labor minimizes Miguel and Jake's total costs? b. What is the optimal amount of capital and labor Miguel and Jake should rent and hire if they plan to spend $12,000 on producing reams of paper each week? c. How many reams of paper will they be able to produce?