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Manuela has $27 to spend on food. She uses it to buy hamburgers and frozen pizzas. The table below shows Manuela's marginal utility (MU) for both hamburgers and frozen pizzas.  Assume that Manuela is a rational consumer who wants to maximize her utility. Suppose that the price of a hamburger has increased to $7 while the price of a frozen pizza remains at $4, Manuela will choose to buy  ____ hamburgers.  Hint:  You will need to calculate marginal utility per dollar spent (MU/P) for both hamburgers and pizza.
 

To determine how many hamburgers Manuela will buy, we need to calculate the marginal utility per dollar spent (MU/P) for both hamburgers and frozen pizzas.

**Step-by-Step Approach:**
1. **Calculate MU/P for each quantity of hamburgers and frozen pizzas:**
   \[
   MU/P = \frac{\text{Marginal Utility}}{\text{Price}}
   \]
   - The price of a hamburger is now $7.
   - The price of a frozen pizza remains $4.

2. **Use the provided marginal utility values to compute MU/P:**
   
   For hamburgers:
   - $ MU/P_1 = \frac{30}{7} \approx 4.29 $
   - $ MU/P_2 = \frac{25}{7} \approx 3.57 $
   - $ MU/P_3 = \frac{20}{7} \approx 2.86 $
   - $ MU/P_4 = \frac{15}{7} \approx 2.14 $
   - $ MU/P_5 = \frac{10}{7} \approx 1.43 $
   
   For frozen pizzas:
   - $ MU/P_1 = \frac{18}{4} = 4.50 $
   - $ MU/P_2 = \frac{16}{4} = 4.00 $
   - $ MU/P_3 = \frac{14}{4} = 3.50 $
   - $ MU/P_4 = \frac{12}{4} = 3.00 $
   - $ MU/P_5 = \frac{10}{4} = 2.50 $

3. **Determine the optimal number of hamburgers and pizzas to maximize total utility:**
   Since Manuela is trying to maximize utility, she will spend her money on the food item that provides the highest marginal utility per dollar (MU/P), starting from the highest value and working down, as long as she stays within her $27 budget.

Let me calculate how much she can buy.Manuela will choose to buy **2 hamburgers** and **3 frozen pizzas**, which will leave her with $26 spent out of her $27 budget.

Would you like more details on the calculations or have any other questions?

Here are five related questions you could explore:
1. What would happen if the price of hamburgers decreased to $5?
2. How would the choices change if Manuela had a budget of $35 instead of $27?
3. What is the impact on utility if the price of pizzas increased to $6?
4. Can you calculate the total utility Manuela gains from buying 2 hamburgers and 3 pizzas?
5. How would Manuela's consumption change if her preferences (marginal utility values) shifted?

**Tip:** Always compare the marginal utility per dollar across different products to maximize utility within a budget constraint.

Manuela has $27 to spend on food. She uses it to buy hamburgers and frozen pizzas. The table below shows Manuela's marginal utility (MU) for both hamburgers and frozen pizzas.  Assume that Manuela is a rational consumer who wants to maximize her utility. Suppose that the price of a hamburger has increased to $7 while the price of a frozen pizza remains at $4, Manuela will choose to buy ____ hamburgers.

Learn how to calculate the marginal utility per dollar spent (MU/P) for hamburgers and frozen pizzas. Manuela has $27 to spend, and with price changes, we'll determine the optimal combination of hamburgers and pizzas to maximize her utility.

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