Question
The annual total revenue for a product is given by
dollars, where
is the number of units sold. To maximize revenue, how many units must be sold? What is the
maximum possible annual revenue?
To maximize revenue,
units must be sold.
(Simplify your answer.)
maximum possible annual revenue?
To maximize revenue,
(Simplify your answer.)
Ask by Wyatt Christensen. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To maximize revenue, 4,500 units must be sold, and the maximum possible annual revenue is $101,250,000.
Solution
To maximize revenue, we need to find the number of units
that maximizes the revenue function:
This is a quadratic function of the form
, where:
-
(since the coefficient of is negative, the parabola opens downward, indicating a maximum point) -
The number of units
that maximizes the revenue can be found using the vertex formula for a parabola:
Plugging in the values:
So, 4,500 units must be sold to maximize revenue.
Next, to find the maximum possible annual revenue, substitute
back into the revenue function:
Calculate each term:
Subtract the second term from the first:
Summary:
- To maximize revenue, 4,500 units must be sold.
- The maximum possible annual revenue is $101,250,000.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg


Beyond the Answer
To maximize revenue, we need to find the value of
that maximizes the function
. This is a quadratic function and opens downwards (since the coefficient of
is negative), so its maximum occurs at the vertex. The vertex
can be found using the formula
, where
and
.
Plugging in the values, we get:
To find the maximum possible annual revenue, substitute
back into the revenue function:
Calculating this gives:
Therefore, to maximize revenue, 4,500 units must be sold, leading to a maximum revenue of $101,250,000.