Math Problem Statement
It has been determined that the cost of producing x units of a certain item is 8x+720 . The demand function is given by p=D(x)=41−0.3x .
Step 1 of 2 : Find the revenue function.
Solution
The revenue function is found by multiplying the price per unit by the number of units sold .
The demand function, which gives the price per unit, is .
Thus, the revenue function is:
Substitute into the equation:
Simplify the expression:
So, the revenue function is:
Would you like further details or have any questions?
Here are 5 related questions to explore further:
- How do we find the profit function using the revenue and cost functions?
- At what value of is the revenue maximized?
- What is the marginal revenue function for this problem?
- How do changes in price affect the revenue function?
- How do you find the break-even point using the cost and revenue functions?
Tip: The maximum revenue typically occurs where the derivative of the revenue function equals zero, as this finds the critical points for maximization.
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Math Problem Analysis
Mathematical Concepts
Algebra
Revenue Function
Demand Function
Quadratic Functions
Formulas
Revenue Function: R(x) = x * p(x)
Demand Function: p(x) = 41 - 0.3x
Theorems
Multiplication of Functions
Suitable Grade Level
Grades 10-12
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