QuestionFind the unit price that maximizes revenue given . What is the maximum revenue?
Studdy Solution
STEP 1
Assumptions1. The revenue function is given by
. We are looking for the unit price that maximizes the revenue
3. We assume that the revenue function is a continuous function over the domain of all possible prices
STEP 2
The revenue function is a quadratic function, which takes the form . The maximum or minimum of a quadratic function occurs at the vertex, which can be found using the formula .
STEP 3
In this case, the coefficients are and . We can plug these values into the formula to find the price that maximizes revenue.
STEP 4
Substitute the values of and into the equation.
STEP 5
Calculate the value of .
STEP 6
The unit price that maximizes revenue is dollars.
STEP 7
Now, we need to find the maximum revenue. We can do this by substituting the value of that maximizes revenue into the revenue function .
STEP 8
Substitute into the equation.
STEP 9
Calculate the value of .
The maximum revenue is dollars.
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