Part $1$: Reliability & Maintenance

A small garage in Northern Ontario has experienced several times power outage last month,

which caused work interruption and delays. The owner is searching out to buy a backup power

generator, and he needs to decide whether to purchase the generator from Supplier A or Supplier

B$.$ The two suppliers have provided the following mean time between failures $($MTBF$)$ and mean

time to repair $($MTTR$)$ information for their product.

a$.$ On the basis of system availability $($SA$),$ which supplier should be selected?

b$.$ Based on the SA of the two generators, what other factors the owner may also consider

when making the purchase decision?

Part $2$: Linear Programming

Suppose that you are considering investing some of your money $($$$10,000)$ into two assets:

government bonds and the stock market. You anticipate that the return rate for government bond

is $10\%$ and for the stock market is $20\%.$ Since the stock market is riskier, you do not want to put

more than $$4,000$ in it$.$ Similarly, you plan to spend at least $$3,000$ on the government bonds.

What will be your investment portfolio in order to maximize your total return? $($Assume all for