Please solve attached problem and show all work, thank you.

It is a time prior to the arrival of House Atreides on Dune. Stilgar, a Fremen leader, needs to plan carefully to optimize his people's use and reuse of water for the coming week. Five gallons have been reclaimed from last week, for example, from the stillsuits that his people wear (to reclaim water expelled from their bodies). Stilgar also has the ability to purchase up to ten gallons of fresh water from town, which has been own in from a nearby planet. Each gallon of fresh water costs two solari (the unit of currency on Dune, and in the Imperium in general), and Stilgar has 16 solari available to spend. Stilgar needs water for various purposes over the coming week. First, he needs enough to cover the nourishment needs of his people, keeping in mind that fresh water offers three times as much nourishment as reused water (since the latter has already lost some of its minerals that his people are only able to get on Dune through water intake). Overall, he would need 6% gallons of fresh water for his people or 19 gallons of reused water for his peoplebut he could use some combination of fresh water and reused water for this purpose, if that would be better. He also needs one gallon of water for cleaning; fresh water and reused water are equally good for this purpose. Finally, he needs two gallons of water for the small number of crops that his people are able to grow for food; only fresh water can be used for this purpose. Stilgar's goal is to minimize the amount of fresh water that he needs to purchase, subject to all of the considerations that have been mentioned. (a) (6 points) Formulate a linear optimization problem that Stilgar can solve to opti- mize his (re)use of water. (Hint: Dene a decision variable for each combination of type of waterLa, reused or freshand use of the water.)