## How much will hiring these inputs cost them?

Miguel and Jake 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 = 4K^0 · 75 x L ^0.25 , 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 MP L = K^0 · 75 / L^0 · 75 and the MP K = 3L^0 · 25 / K^0 · 25 . The weekly cost function for the paper plant is C = 1 OK + 2L, where C is the total weekly cost. a. What ratio of capital to labor minimizes Miguel and Jake's total costs? b. How much capital and labor will Miguel and Jake 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?

### f you think there are good arguments for, or a proof of, God’s existence, state the arguments or the proof and defend it against your atheist friend’s objections.

If you believe in God, try to explain to an atheist friend (real or imagined) why you believe in God. • If you think there are good reasons for believing,….

### Choose one of the elements defended by the pre-Socratic philosophers (water, fire, numbers, and so on) and argue for it as well as you can, preferably with a friend or a few friends who will try to prove you wrong.

Choose one of the elements defended by the pre-Socratic philosophers (water, fire, numbers, and so on) and argue for it as well as you can, preferably with a friend or….

### What is the net present value of the proposed mining project? Should the project be accepted?

Net Present Value Analysis Windhoek Mines, Ltd., of Namibia, is contemplating the purchase of equipment to exploit a mineral deposit on land to which the company has mineral rights. An….