Suppose that the production function for ipods isq 20k05l05

Question

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 isQ= 4K^0.75L^0.25whereQis the number of reams produced,Kis the quantity of capital rented, andLis the quantity of labor hired. For this production function, theMP_L=K^0.75/L^0.75and theMP_K= 3L^0.25/K^0.25. The weekly cost function for the paper plant isC= 10K+ 2L, whereCis the total weekly cost. How much will it cost Jake and Paul to produce 1,000 reams of paper each week if they are minimizing their total costs?

Suppose that the production function for iPods isQ= 20K^0.5L^0.5. The marginal product of labor is 10(K/L)^0.5, and the marginal product of capital is 10(L/K)^0.5. Suppose that labor can be hired for $6, and capital can be rented for $9. If the firm has exactly $300 to spend on producing iPods, what is the maximum number of iPods it can produce