The Martinez twins, Carlos and Clarita are trying to find a way to make money during summer vacation. When they overhear their aunt complaining about how difficult it is to find someone to care for her pets while she will be away on a trip, Carlos and Clarita know they have found the perfect solution. Not only do they have a large, unused storage shed on their property where they can house animals, they also have a spacious fenced backyard where the pets can play. Carlos and Clarita are making a list of some of the issues they need to consider as part of their business plan to care for cats and dogs while their owners are on vacation. *Space: Cat pens will require 6 ft² of space, while dog runs require 30 ft². Carlos and Clarita have up to 360 ft² available in the storage shed for pens and runs, while still leaving enough room to move around the cages. *Start-up Costs: Carlos and Clarita plan to invest much of the $1000 they earned from their last business venture to purchase cat pens and dog runs. It will cost $32 for each cat pen and $65 for each dog run. 1) TO DO: Let x = # of dogs and y = # of cats. Write a system of inequalities: a) Reflecting space limitations b) Reflecting start-up costs c) x ≥ 0 and y ≥ 0 2) TO DO: Graph the system of inequalities using the graphing tools at http://www.desmos.com. Zoom in on the region reflecting possible combinations for the number of cats and dogs that meet the limitations. Click on the corner points of the feasibility region (there should be 4 corner points!). Write the coordinates of these corner points down. Of course, Carlos and Clarita want to make as much money as possible from their business, so they are trying to determine how many of each type of pet they should plan to accommodate. They plan to charge $10 per day for boarding each cat and $20 per day for each dog. After surveying the community regarding the pet boarding needs, Carlos and Clarita are confident that they can keep all of their boarding spaces filled for the summer. So the question is, how many of each type of pet should they prepare for? [When answering the questions, keep in mind that you cannot have a fractional number of pets! You'll have to round down... For example, if the graph looks like you can have 3 dogs and 2.5 cats, you'd have to say 3 dogs and 2 cats for your calculations.