Hi, I've been struggling with this part of the chapter for a few hours now and would appreciate some help.
Last year Jerry's Tents sold 150 tents for $550 each. The manager estimates that for each $50 increase in price, the number sold will decrease by 5.
A) Represent the number of tents sold, n , as a function of the selling price, s dollars.
B) Represent the revenue, R dollars, as a function of the selling price.
C) What is the maximum revenue?
D) What selling price produces maximum revenue?
E) What range of selling prices will provide revenue greater than $100 000?
I just wrote all the questions down so you could understand how the question is supposed to be answered. I don't get anything after part C.
Sorry the answer comes so late,
so we have a function : changing the price has an influence on the number of tents sold so the price P of one tent is the x variable and the number sold N is the y variable. N is a function of P.
This is linear :
We write the points (x,y) as being (P,N)
we have (550$,150) and then (600$,145),(650$,140)... If you draw the points you'll see it is linear. The slope can be taken for any two points since the function is linear and the slope is always the same.
We take the two points (550$,150) and (600$,145)
slope = (145-150)/(600-550)=-5/50=-0.1
So N = -0.1 P + b where b is not known (intersection with the y axes). We replace by one of the points :
150 = -0.1 * 550 + b so we isolate b and get b=205. So N=-0.1 P + 205.
Some info about how they calculate their revenue is missing to continue the answer.