The Martinex twins, Carlos and Clarita, are trying to find a way to make money during the 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 Clarity 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.

A:Cat pens will require 6ft2 of space, while dog runs require 24ft2. Carlos and Clarita have up to 360ft2 available in the storage shed for pens and runs, while still leaving enough room to move around the cages.
Utilize the information about space available to write a two variable equation to represent the amount of space used for boarding the cats and dogs. Start-up Costs: Carlos and Clarita plan to invest much of the $1280 they earned from their last business venture to purchase cat pens and dog runs. It will cost $32 for each cat pen and $80 for each dog run. Write a two variable equation to represent the start-up costs for boarding the cats and dogs. and
Graph the two equations one the same x, y plane in Desmos

B: Clarita and Carlos realize after looking at the graphed equation models they do not have to use all of the available space nor do they need to use all of the start up money. They decide to explore a system where they can better visualize and plan for up to and including the available space and start up funds.

Change your original equations into inequalities
is screenshot

C:
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 $8 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? Their dad has suggested the same number of each, perhaps 12 cats and 12 dogs. Would the dad’s suggestion be possible? Why or why not?