I need help with linear programming: The shelter has space for up to 25 dogs...

l.mo

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Oct 17, 2018
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I have done some problems, but I’m stuck on 2 of them. The first is this:
An animal shelter cares for both dogs and cats until they get adopted. The shelter has space for up to 25 dogs as well as a separate space for up to 45 cats. Each dog takes up 3 units of space at the shelter while each car takes up 1 unit of space. What combination allows the shelter to maximize the amount of animals they take care of?

I defined the variables as
x: dogs
y:cats

i need to find the constraints to graph them. i have 3 so far that I think are correct but I don’t know what to do with the info about the space they take up. The constraints I have are
x less than or equal to 25
y less than or equal to 45
x + y less than or equal to 70 (the maximum cats plus max dogs)

i also need the objective function. Right now I have x + y = animals but i don’t think that’s right.
 
Frankly, the information given simply doesn't make sense. We are told that there is "space for up to 25 dogs" and "separate space for up to 45 cats". Since the spaces are separate I don't see how "Each dog takes up 3 units of space at the shelter while each car takes up 1 unit of space" gives us any useful information. If those spaces are separate then decreasing the number of dogs would not increase the possible number of cats nor vice-versa.
 
An animal shelter cares for both dogs and cats until they get adopted.
The shelter has space for up to 25 dogs
as well as a separate space for up to 45 cats.
Each dog takes up 3 units of space at the shelter
while each cat takes up 1 unit of space.
What combination allows the shelter to maximize the amount of animals they take care of?
As worded, answer is 25 + 45 = 70 ; simply both at capacity...
 
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