option 2: 5 marks\njaxon sells subscriptions for mathflix, a streaming service which provides math videos to…

option 2: 5 marks\njaxon sells subscriptions for mathflix, a streaming service which provides math videos to help struggling students, for $8.10 per month. at this price, there are 300 subscribers each month. for every $.05 decrease in the price, 30 more students will purchase a subscription. what price should be charged to produce maximum revenue?

option 2: 5 marks\njaxon sells subscriptions for mathflix, a streaming service which provides math videos to help struggling students, for $8.10 per month. at this price, there are 300 subscribers each month. for every $.05 decrease in the price, 30 more students will purchase a subscription. what price should be charged to produce maximum revenue?

Answer

Explanation:

Step1: Define variables

Let ( x ) be the number of ($0.05) decreases in price. The price per subscription ( p=(8.10 - 0.05x)) dollars. The number of subscribers ( n=(300 + 30x))

Step2: Revenue function

Revenue ( R = p\times n=(8.10 - 0.05x)(300 + 30x)) Expand the function: [ \begin{align*} R&=8.10\times(300 + 30x)-0.05x\times(300 + 30x)\ &=2430+243x - 15x-1.5x^{2}\ &=- 1.5x^{2}+228x + 2430 \end{align*} ]

Step3: Find the vertex of the quadratic function

For a quadratic function (y = ax^{2}+bx + c) ((a=-1.5), (b = 228), (c = 2430)), the (x) - coordinate of the vertex is (x=-\frac{b}{2a}) [ x=-\frac{228}{2\times(-1.5)}=\frac{228}{3}=76 ]

Step4: Calculate the price

Substitute (x = 76) into the price formula (p=(8.10 - 0.05x)) [ p=8.10-0.05\times76=8.10 - 3.80=4.3 ]

Answer:

The price that should be charged to produce maximum revenue is ($4.30)