You sell candy at an event to make money.  When candy are sold for $1.10 per bag, approximately 625 bags are sold at each event.  You tried to raise the price to $1.35 and found that the quantity demanded dropped to 525 bags.  The startup cost was $500 and the cost to you per bag of peanuts is $0.50.     Assume that the demand function is linear and write a function that models the profit from selling x bags of peanuts at an event.     What number of bags and what price per bag will get you a maximum profit?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.