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.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your formula is:
y = (600 - 30x) * (6 + .5x)
y is the revenue
600 - 30x tells you the number of new subscriptions sold each week.
6 + .5x tells you the price of each new subscription, in dollars.
the value of x tells you the number of times you are subtracting 30 from 600 and adding .5 to 6.
when x = 0, the number of subscriptions remains at 600 and the price remains at 6 and the revenue becomes 600 * 6 = 3600.
when x = 1, the number of subscriptions becomes 570 and the price per subscription becomes 6.5 and the revenue becomes 570 * 6.5 = 3705.
y = (600 - 30x) * (6 + .5x) is a quadratic equation.
the standard form of this equation is y = -15x^2 + 120x + 3600
with the equation in standard form, a is the coefficient of the x^2 term and b is the coefficient of the x term and c is the constant term.
the maximum value of this quadratic equation is when x = -b / 2a
that becomes -120 / -30 = 4.
when x = 4, y = -15x^2 + 120x + 3600 becomes y = -15 * 16 + 120 * 4 + 3600 which becomes -240 + 480 + 3600 = 3840.
this can be seen in the graph of the two equivalent equations.
because they are equivalent, they draw the same curve on the graph.
the two equivalent equations are:
y = (600 - 30x) * (6 + .5x)
y = -15x^2 + 120x + 3600
here's the graph.
Answer by MathTherapy(10552)  (Show Source):
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