If the revenue function for a particular commodity is
R(p) = −53p2 + 68p,
what is the (linear) demand function q(p)?
q(p) =

The revenue function is given by:

\[
R(p) = -53p^2 + 68p
\]

Revenue \(R(p)\) is the product of the price \(p\) and the quantity demanded \(q(p)\), i.e.,

\[
R(p) = p \cdot q(p)
\]

So, to find the demand function \(q(p)\), we can solve for \(q(p)\):

\[
q(p) = \frac{R(p)}{p} = \frac{-53p^2 + 68p}{p}
\]

Simplifying the right-hand side:

\[
q(p) = -53p + 68
\]

Thus, the linear demand function is:

\[
q(p) = -53p + 68
\]

Would you like further clarification or more details on any step?

Here are 5 related questions to deepen your understanding:
1. What happens to the quantity demanded when the price increases?
2. How would you calculate the equilibrium price given a cost function?
3. What is the maximum revenue, and at what price does it occur?
4. How do you derive the inverse demand function from the demand function?
5. How does elasticity of demand relate to the demand function?

**Tip**: The demand function shows the relationship between price and quantity demanded. When it's linear, the slope gives the rate of change in demand relative to price.

If the revenue function for a particular commodity is R(p) = −53p^2 + 68p, what is the (linear) demand function q(p)?

Learn how to derive the linear demand function q(p) from the revenue function R(p) = −53p^2 + 68p. This problem covers key algebraic concepts related to revenue and demand functions, suitable for students in Grades 10-12.

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