Lavro operates a popular hotdog stand. He sells 320 sausages per day at a price of $5.50 each. The previous year's sales show that for every $0.50 decrease in price, he
will sell another 40 sausages.
The equation that models this problem is:
R(x) = (price)
(number sold)
R(x) = (5.50 - 0.50x)(320 + 40x)
Question 3 (1 point)
What is his maximize potential revenue?

Given:

Lavro sells 320 sausages per day at a price of $5.50 each.

The previous year's sales show that for every $0.50 decrease in price, he  will sell another 40 sausages.

The equation that models this problem is:

To find:

The maximum potential revenue.

Solution:

We have,

It can be written as:

Differentiate with respect to x.

For critical points, .

Differentiate R'(x) with respect to x.

Since R''(x)<0, therefore function R(x) is maximum at . The maximum value is:

Therefore, the maximize potential revenue is $1805 at .

y - y1 = m(x- x1)

y - (-5) = 2/3(x -0)

y + 5 = 2/3x

y = 2/3x - 5