Save the pups!

One of the world's most adorable marine mammals is at risk of extinction. Your marine mammal research team has received a $1,000 grant to carry out an intervention to increase its population by this time next year. Your goal then is to maximize the population one year from now, hoping to publish a breakthrough paper and get more funding to do a bigger project to save the species.

Based on your research data, your team estimates that if M gallons of medicine and N gallons of nutrients are added to their marine habitat, then by next year this will save M2 + NM + 12N lives. (The habitat is huge, so there is no need to worry about "overdose"). A gallon of medicine costs $25 and a gallon of nutrients costs $5.

(a) What is the cost of M gallons of medicine and N gallons of nutrients?
(b) To maximize, within your budget, the number of lives saved by next year, which combinations of medicine and nutrients would you consider putting into the habitat?
(c) Which combination would you use? How many adorable marine mammals will you have saved by this time next year?

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