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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. If the price of a hamburger is $5 and the price of a frozen pizza is $4, Manuela will choose to buy____ frozen pizzas.  Hint:  You will need to calculate marginal utility per dollar spent (MU/P) for both hamburgers and pizza.

To determine how many frozen pizzas Manuela will buy, we need to calculate the marginal utility per dollar spent (MU/P) for both hamburgers and pizzas, and then allocate her $27 in a way that maximizes her total utility.

### Step 1: Calculate MU/P for each quantity of hamburgers and pizzas.

The price of a hamburger is $5, and the price of a frozen pizza is $4. Let's calculate the MU/P for each level of consumption.

#### MU/P for Hamburgers:
- For 1 hamburger: $ MU/P = \frac{30}{5} = 6 $
- For 2 hamburgers: $ MU/P = \frac{25}{5} = 5 $
- For 3 hamburgers: $ MU/P = \frac{20}{5} = 4 $
- For 4 hamburgers: $ MU/P = \frac{15}{5} = 3 $
- For 5 hamburgers: $ MU/P = \frac{10}{5} = 2 $

#### MU/P for Frozen Pizzas:
- For 1 pizza: $ MU/P = \frac{18}{4} = 4.5 $
- For 2 pizzas: $ MU/P = \frac{16}{4} = 4 $
- For 3 pizzas: $ MU/P = \frac{14}{4} = 3.5 $
- For 4 pizzas: $ MU/P = \frac{12}{4} = 3 $
- For 5 pizzas: $ MU/P = \frac{10}{4} = 2.5 $

### Step 2: Compare MU/P values and allocate budget.

Manuela has $27 to spend, so she needs to choose combinations of hamburgers and pizzas that provide the highest marginal utility per dollar. We will compare the MU/P of hamburgers and pizzas at each step and allocate her budget accordingly.

### Decision Process:
- **First dollar**: MU/P for 1 hamburger is 6, for 1 pizza is 4.5. She will buy 1 hamburger (cost = $5).
- **Remaining $22**: After buying 1 hamburger, she has $22 left. Next, MU/P for 2 hamburgers is 5, for 1 pizza is 4.5. She will buy another hamburger (cost = $5).
- **Remaining $17**: After buying 2 hamburgers, she has $17 left. MU/P for 3 hamburgers is 4, for 1 pizza is 4.5. She will buy 1 pizza (cost = $4).
- **Remaining $13**: After buying 1 pizza, she has $13 left. MU/P for 3 hamburgers is 4, for 2 pizzas is 4. She can choose either 1 more hamburger or 1 more pizza. She will buy 1 more hamburger (cost = $5).
- **Remaining $8**: After buying 3 hamburgers and 1 pizza, she has $8 left. MU/P for 4 hamburgers is 3, for 2 pizzas is 4. She will buy 1 more pizza (cost = $4).
- **Remaining $4**: With $4 left, MU/P for 4 hamburgers is 3, for 3 pizzas is 3.5. She will buy 1 more pizza (cost = $4).

### Final Purchase:
Manuela will buy:
- **3 hamburgers**
- **3 frozen pizzas**

Thus, she will choose to buy **3 frozen pizzas**.

Would you like more details or further explanation on this process?

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### Related Questions:
1. What is the total utility Manuela derives from her purchase of hamburgers and pizzas?
2. How does the marginal utility per dollar change with each additional hamburger or pizza?
3. What would happen if the price of hamburgers or pizzas changed? How would her consumption choices be affected?
4. What is the significance of diminishing marginal utility in this scenario?
5. How would her choices change if she had a larger budget of $35?

### Tip:
When trying to maximize utility, always compare the marginal utility per dollar of each option and allocate your budget toward the option with the highest value.

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. If the price of a hamburger is $5 and the price of a frozen pizza is $4, Manuela will choose to buy____ frozen pizzas. Hint: You will need to calculate marginal utility per dollar spent (MU/P) for both hamburgers and pizza.

Discover how Manuela optimizes her $27 budget to maximize her utility by purchasing hamburgers and frozen pizzas. This problem explores key economic concepts such as marginal utility, budget allocation, and the law of diminishing marginal utility. Ideal for students in Grades 11-12.

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