Questions: Exercise 9 - Find the marginal revenue if the price p and demand x are related by p=750-0.3 * x.

Transcript text: Exercise 9 - Find the marginal revenue if the price $p$ and demand $x$ are related by $p=750-0.3 \cdot x$.

Solution

Solution Steps

To find the marginal revenue, we first need to express the revenue $ R $ as a function of demand $ x $. Revenue is calculated as the product of price $ p $ and demand $ x $, i.e., $ R = p \cdot x $. Given the relationship between price and demand, substitute $ p = 750 - 0.3x $ into the revenue function. Then, differentiate the revenue function with respect to $ x $ to find the marginal revenue.

Step 1: Define the Price Function

The relationship between price $ p $ and demand $ x $ is given by the equation: \[ p = 750 - 0.3x \]

Step 2: Define the Revenue Function

Revenue $ R $ is calculated as the product of price and demand: \[ R = p \cdot x = (750 - 0.3x) \cdot x = 750x - 0.3x^2 \]

Step 3: Calculate the Marginal Revenue

To find the marginal revenue, we differentiate the revenue function $ R $ with respect to $ x $: \[ \frac{dR}{dx} = 750 - 0.6x \] Thus, the marginal revenue is given by: \[ MR = 750 - 0.6x \]