Jake and Paul run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is Q = 4K0.75L0.25, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. For this production function, the MPL = K0.75/L0.75 and the MPK = 3L0.25/K0.25. The weekly cost function for the paper plant is C = 10K + 2L, where C is the total weekly cost.
a. What ratio of capital to labor minimizes Jake and Paul's total costs?
b. How much capital and labor will Jake and Paul need to rent and hire in order to produce 1,000 reams of paper each week?
c. How much will hiring these inputs cost them?