suppose a pizzeria appropriatley name s"MPA = Master's of Pizza Administrations" (which has unfortunately occasionally been confused with the "Master's of Propane Administration") sells 500 chsse Pizza when the price is $10/ pizza and 1100 cheese pizzas when the price is $8/ pizza.

To analyze this scenario, we can model the relationship between the price of the cheese pizza and the quantity sold using a linear demand function. The general form of a linear demand equation is:

\[
Q_d = a - bP
\]

Where:
- $Q_d$ is the quantity demanded.
- $P$ is the price.
- $a$ and $b$ are constants.

Given the information:
- When $P = 10$, $Q_d = 500$.
- When $P = 8$, $Q_d = 1100$.

We can set up two equations based on the given data to solve for $a$ and $b$.

1. For $P = 10$ and $Q_d = 500$:
   \[
   500 = a - 10b \quad \text{(Equation 1)}
   \]
2. For $P = 8$ and $Q_d = 1100$:
   \[
   1100 = a - 8b \quad \text{(Equation 2)}
   \]

Now, we can solve these two equations simultaneously to find the values of $a$ and $b$.

**Step 1: Subtract Equation 1 from Equation 2**

\[
(1100 - 500) = (a - 8b) - (a - 10b)
\]
\[
600 = 2b
\]
\[
b = 300
\]

**Step 2: Substitute $b = 300$ into Equation 1 to find $a$**

\[
500 = a - 10(300)
\]
\[
500 = a - 3000
\]
\[
a = 3500
\]

So, the demand equation is:

\[
Q_d = 3500 - 300P
\]

### Interpretation
- The demand function $Q_d = 3500 - 300P$ indicates that as the price increases by $1, the number of pizzas sold decreases by 300.
- At a price of $0 (hypothetical), the maximum quantity demanded would be 3500 pizzas.

### Would you like to go into more details, or do you have any questions about this?

Here are 5 related questions for further exploration:
1. What is the revenue function for the pizzeria based on this demand equation?
2. How many pizzas would be sold if the price were set to $9?
3. What price should the pizzeria charge to maximize revenue?
4. How would an increase in the price elasticity of demand affect the pizzeria's pricing strategy?
5. Can this demand model be used to predict the effect of a discount on sales during a promotion?

**Tip:** Understanding the demand function helps businesses determine the optimal pricing strategy to maximize revenue and market share.

Suppose a pizzeria appropriately named 'MPA = Master's of Pizza Administrations' (which has unfortunately occasionally been confused with the 'Master's of Propane Administration') sells 500 cheese pizzas when the price is $10/pizza and 1100 cheese pizzas when the price is $8/pizza.

Analyze how a pizzeria named 'MPA' models the relationship between price and quantity sold using a linear demand function. This problem provides a step-by-step solution for calculating the demand equation based on sales data at two different prices. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation