Question 1173633
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.
<pre>Quadratic equation: {{{matrix(2,3, y, "=", (600 - 30x)(6 + .5x), y, "=", "3,600" + 120x - 15x^2)}}}
Now, you need to COMPLETE the SQUARE to find the solutions/roots to/of the quadratic! 
Then, from the above you need to also solve using the Quadratic Equation formula: {{{matrix(1,3, x, "=", (- b +- sqrt(b^2 - 4ac))/(2a))}}}.
I don't know why but that's what's been asked!
Correct answers: <b>a)</b> Four (4) $0.50 increases will yield maximum weekly revenue. Thus, to obtain the maximum weekly revenue, price MUST BE {{{highlight_green(matrix(1,5, 6 + 4(.5), "=", 6 + 2, "=", "$8"))}}}
                 <b>b)</b> Number of subscriptions that needs to be sold in order to achieve maximum revenue: {{{highlight_green(matrix(1,5, 600 - 4(30), "=", 600 - 120, "=", 480))}}}