1. Inspired by one too many late nights of Stardew Valley, you've decided to become a farmer! You grow plums ), and to make some extra money you make a handful of delicious things out of your plums: plum tarts ), plum jam (), and plum pudding Over your first few months of farming, you've noticed the following things: Picking plums is tiring work! For every 100 plums you pick, you come home starving and eat 2 slices of tart and 2 plum puddings To make a plum tart, which gives you 10 slices of tart, you need to use 5 plums and 1 jar of jam To make 10 jars of jam , you need 100 plums ; you also need 1 slice of tart because you get bored and want something to snack on while the jam stews. Each individual plum pudding you serve uses up a plum and comes with a healthy dollop of jam; so, to make 1 plum pudding you need to use 1 plum and jar of jam. (a) Suppose that you want to bring 900 plums, 30 slices of tart, 30 jars of jam, and 60 plum puddings to the farmer's market. To do this, how many plums do you need to pick/tarts, jams, and plum puddings do you need to make? (b) In the above scenario, we said that when we made a slice of tart, we used up a plum, when we made a jar of jam we used up 10 plums, and when we made a plum pudding we used up 1 plum. Suppose we changed this scenario to one in which making a slice of tart uses a plums, mak- ing a jar of jam uses 3 plums, and making a plum pudding uses y plums, and we still have the same target goal of 900 plums, 30 slices of tart, 30 jars of jam, and 60 plum puddings from (a). Is there a triple of values a, B, y in R such that it would be mathematically impossible' for us to solve the resulting system of linear equations? Either find such values and explain why the resulting system of linear equations has no solutions, or prove that no such values can exist.