A company has developed a new digital picture frame Test mar

A company has developed a new digital picture frame. Test market data has indicated that the revenue from sales of the frame is given by R(p)= -10p^2+1580p, where p is the price per unit (in dollars).
A. What price will yield the maximum revenue?
B. What is the maximum revenue?

Solution

Here you would just need to differentiate the equation by p so the differentiation will be R\'=-20p+1580 and when this is equal to zero, it gives us the price,p where it will yield maximum value. This is because the double differentiation of R i.e R\'\' by p is -20 which is -ve. A negative R\'\' will always mean that the R is maximum when R\'\' is -ve . Now the value of p at which R\' is 0 is p=1580/20=79 Hence, answer A is 79 and this gives us the maximum value of R(p) which is R(79) i.e -10(79)^2+1580x79=62410. This is answer B