The total revenue R earned in thousands of dollars from manu

The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by R(p) = -25p^2 + 1700p where p Is the price per unit (in dollars). Find the unit price that will yield a maximum revenue.

Solution

Let y = R(p) = -25p² + 1700p. For y = R (p) to be maximum, dy/dp = 0 or, -50p + 1700 = 0, or, 50p = 1700 or,

p = $ 34. Thus the unit price that will yield the maximum revenue is $ 34. We can verify the result by substituting three values of p viz. $ 33, 34 and 35.