S$)$ Queues$-$this happens when an entity can't move, so resources are not available it has to wait. V

Question $2$

$[22]$

The RandWater supplies water to a large municipal area. The process of purifying water starts with primary disinfection carried out at the water treatment plants and secondary disinfection at the booster pumping stations. After sedimentation and filtration all water is disinfected with chlorine before being put into the distribution system. The secondary phase of the disinfection process requires $300$ kilo$-$volt$-$amperes $($kVA$)$ generators to effectively purify the water. Management recognizes that even a well$-$maintained generator will have periodic breakdowns. Energy demands over the past $4$ years have been consistently high, and the company is concerned over downtime of generators. It currently employs three highly skilled repair technicians at $R{45}_{?}$ per hour. Each work $8-$hour shift. In this way, there is always a repairperson on duty $24$ hours a day, $7$ days a week.

For each hour that one of the generators is down, RandWater loses roughly R$105.$ This amount is the charge for reserve power that RandWater must "borrow" from the neighbouring utility company. Table $1$ shows the Time between machine failure and the number of times observed while Table $2$ shows repair time required and number of times observed:

Table $1$: Machine Failure

$\backslash$table$[[\backslash$table$[[$Time between recorded machine failure$],[($Hours$)]],\backslash$table$[[$Number of times$],[$observed$]]],[0\mathrm{.}5,6],[1\mathrm{.}0,7],[1\mathrm{.}5,17],[2\mathrm{.}0,34],[2\mathrm{.}5,22],[3\mathrm{.}0,20]]$

Table $2$: Repair Time

$\backslash$table$[[\backslash$table$[[$Repair time required$],[($Hours$)]],$Number of times observed$],[1,30],[2,54],[3,22]]$

You have been assigned to conduct a management analysis of the breakdown problem. You realise that simulation is a workable tool because of the probabilistic nature of this problem.

As a potential system analyst:

$($a$)$ Simulate $10$ machine failures occurrence, assuming that the first day begins at $08$:$00$ AM$.$ Note that you are expected to select random number for machine failure from the third