$10.$ What are some major capacity considerations in a hospital? How do they differ from those of a car manufacturing factory?

$11.$ A factory has a maximum capacity of $5,000$ units per day using overtime and skipping the daily maintenance routine. At $4,000$ units per day, the factory operates at a level where the average cost per unit is minimized. Currently, the operation runs at a level of $3,500$ units per day. What is the capacity utilization rate?

$12.$ In considering a capacity expansion at a battery company, we have two alternatives:

$1.$ The first alternative is expected to cost $$1,000,000$ and has an expected profit of $$500,000$ per year over the next three years.

$2.$ The second alternative is expected to cost $$800,000$ and has an expected profit of $$450,000$ per year over the next three years.

Currently, the interest rate is $10\%,$ and at that rate, the present value of $$1$ in the following three years is: $0\mathrm{.}909,0\mathrm{.}826,$ and $0\mathrm{.}751,$ respectively. Which alternative should we select, and what is the expected value of the expansion.