Two college students earn extra money on weekends by delivering firwood in thier pickup truck. They have found that they can sell x cords per weekend at a price of p dollars per cord, where x=75-3/5 p. The students buy the firewood from a supplier who charges them C dollars for x cords to the equation C=500+15 x+1/5 x2.

a) find a function f such that P=f(p), where P dollars is the profit per weekend for the students if they charge p dollars per cord.

b)find the profit P dollars if p=$95

I am a student at college.

Hi Jackie,

Profit is the amount of money you take in minus the amount you spend. That is profit is revenue minus cost. The cost you know, C=500+15 x+1/5 x2. You also know that x=75-3/5 p so you can substitute this expression into the cost function to express cost as a function of p.

Revenue, R, is the number of cords the students sell times the price they charge for a cord. Thus R = xp. But x=75-3/5 p so R = p(75-3/5 p)

Now you can write P = R - C as a function of p.

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