pls help answer both question and show all work Question $3$: For each of the following problems,

$($i$)$ Determine if the problem is deterministic or stochastic, and

$($ii$)$ Define two appropriate state variables and explain if they are discrete or continuous.

Remember to explain why for full credit.

a$)(6$ points$)$ Chicago hosts Lollapalooza $($music festival$)$ every summer. The organizers have

already figured out which artists and bands will come. But the biggest complaint from

attendees have been not having enough water, food$/$beverage booths or food trucks and

restrooms on site. The organizers want to make sure there are enough food vendors, water

stations, and rest areas so that everyone can enjoy the experience and not wait in long lines.

In $2024,$ they had organizers and volunteers stationed at different places to gather data on

the arrival rate to the venue from morning to night, arrival rate to the food$/$beverage

booths, and arrival rates to restrooms. Based on the list of artists and bands, they anticipate

that there will be $1d\%$ more attendees this time.

b$)(6$ points$)$ A farmer wants to set up a hydroponics farm for some of their crops. A

hydroponics farm consists of growing plants in water. Regularly, fertilizer is added to the

water and other solutions to keep the pH level of the water in a particular range. The water

is recycled every once in awhile and renewed depending on how much water is in the

container and the plants in each one. Hydroponics can be used to plan herbs, tomatoes,

cucumbers, peppers, etc. The goal of the simulation is to determine how much water the

farmer will use, the amount of fertilizer to purchase, and the amount of solution to buy to

maintain the pH level. The corrective solution is added whenever the pH level is out of the

allowable tolerance. The water is changed when a certain level of bacteria is detected.

Because the farm will be in a temperature controlled environment, we can simulate the

approximately growth rate, water evaporation rate, etc.