Question

If the total revenue function for an item is R(x) = 35x - 0.25 x2 , first determine how many units x must be sold of the item in order to produce the maximum total revenue possible for this product and then use this amount to compute the maximum total revenue possible to be generated by this item.

Answer 1

Answer:

So there should be 70 units must be sold for maximum revenue and maximum revenue will be 1225

Explanation:

We have given that the total revenue for an time is given by $R(x)=35x-0.25x^2$

Now for maximum revenue $R'(x)$ must be zero

$R'(x)=35-0.5x$

So $35-0.5x=0$

x = 70

Now maximum revenue will occur at x= 70

So maximum revenue = $=35\times 70-0.25\times 70^2=2450-1225=1225$

So there should be 70 units must be sold for maximum revenue and maximum revenue will be 1225