Question

Yummy Yogurt Manufacturing Co. makes 10 cents per container of plain yogurt that it sells and 12 cents per container of vanilla yogurt. They want to make monthly profit of at most $ 3,200. This month, Yummy expects to sell at most 12,000 cups of plain yogurt (p), but no less than 15,000 cups of vanilla yogurt (v).

Which of the following inequalities represent this situation? Select THREE that apply.

Answer 1

To represent the situation mathematically, we can define the variables as follows:

- Let \( p \) be the number of containers of plain yogurt sold.
- Let \( v \) be the number of containers of vanilla yogurt sold.

The profit from plain yogurt is 10 cents per container, which can be expressed as \( 0.10p \), and the profit from vanilla yogurt is 12 cents per container, which can be expressed as \( 0.12v \).

1. **Profit Constraint**: Yummy Yogurt Manufacturing Co. wants to make a monthly profit of at most $3,200, which translates to the inequality:
\[
0.10p + 0.12v \leq 3200
\]

2. **Sales Constraints for Plain Yogurt**: They expect to sell at most 12,000 containers of plain yogurt, represented as:
\[
p \leq 12000
\]

3. **Sales Constraints for Vanilla Yogurt**: They expect to sell no less than 15,000 containers of vanilla yogurt, represented as:
\[
v \geq 15000
\]

Thus, the inequalities representing the situation are:

- \( 0.10p + 0.12v \leq 3200 \)
- \( p \leq 12000 \)
- \( v \geq 15000 \)

These three inequalities capture the conditions described in the problem.