SOLUTION: QUADRATICS WORD PROBLEM An online, music service called peach music can sell 600 new subscription every week at $6.00per new subscription. The manager is considering increasing th

Question 1173668: QUADRATICS WORD PROBLEM
An online, music service called peach music can sell 600 new subscription every week at $6.00per new subscription. The manager is considering increasing the price. A marketing survey showed that for every $0.50 increase in price, there would be 30 fewer new subscriptions.
If x is the number of price increases and R is the revenue in dollars, this situation cann be moddle by the following equation: R=-15x^2+120x+3600
a) What price should they set per subscription in order to obbtain the maximum weekly revenue?
b)How many subsripton would they sell in order to achive this maximum revenue?
Calculate the necessary values by first completing the square and then the quadratic formula. Show all your work.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
That is correct and comes from
(600-30x)(6+0.5x)
-
-15x2+120x+3600=
-(15x^2-120x) +3600)=
-15(x^2-8x)+3600=
-15(x^2-8x+16)+3600+240, to keep the equation in balance
-15(x-4)^2+3840
This quadratic is now in vertex form, and the vertex is (4, 3840). That means the value of x maximizing the quadratic is 4 and f(x)=3840.
The quadratic formula will find the roots, which are -12 and 20, and the vertex is the axis of symmetry x value in between the roots or 4.
x=-(1/30) (-120+/- sqrt( 14400+216000)); sqrt (230400) is 480
x=-12 and 20.

the price would be $8, and they would sell 480 subscriptions to make $3840.
-
Here is another way to check:
the maximum is when x=-b/2a or -120/-30 or 4
when x is 4
that is 480 subscriptions at $8 for a maximum revenue of $3840.

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