I'm trying to help a student with a word problem and am stuck on it. He's learning how to use functions to find maximum and minimum values for word problems. None of the examples in his text are like the problem below, and we can't figure it out.:
"A publishing company can get 500 subscribers for a weekly news magazine if the yearly subscription rate is $60. The company will get 10 more subscribers for each $1 decrease in the yearly rate. What rate will produce the maximum income, and what will that income be?"
In other problems of this type, we'd say the following:
x = additional subscribers
500 + x = total subscribers
60-x = subscription rate
Then if you solve for the f(x) = (500+x)(60-x) you get an equation that tells the maximum income and also the maximum income. But, in this case it's not $1 per additional subscriber, but per 10 subscribers. What am I doing wrong in my equation then?