3. A video store rents 800 videos per week at $4/video. They did some research and found that for every $0.50 increase in rental price, they will rent 50 less videos.
a) Develop an equation that models the revenue, R, and number of price increases x.
b) What is the maximum revenue they can make
c) How much should they charge per video rental to maximise the revenue?
d) How many videos will they rent for maximum revenue
e) What will be their revenue if the rent for each video is $10 each?
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the equation is Revenue = Price * Units
Price = (4 - .5x)
Units = (800 - 50x)
So when x increases price drops by increments of .5 and Units sold drops by 50
Multiply them and you have your equation Revenue = (4 - .5x)(800 - 50x)
Price should be (4+.5x)
To find where revenue is most take the derivative R(x) = -25x^2 +200x + 3200
R'(x) = -50x + 200
0 = -50x + 200
4 = x, so max at 4