Question

What is the minimum number of units of product C that must be produced to meet the total production requirement of 200 units, given that at least 20 units of A and 30 units of B must be produced?

Answer 1

To determine the minimum number of units of product C that must be produced to meet the total production requirement of 200 units while ensuring at least 20 units of product A and 30 units of product B are produced, we can set up the following equation:

Let:
- \( x \) be the number of units of product A produced,
- \( y \) be the number of units of product B produced,
- \( z \) be the number of units of product C produced.

According to the problem:
1. \( x + y + z = 200 \) (total production requirement)
2. \( x \geq 20 \) (at least 20 units of A)
3. \( y \geq 30 \) (at least 30 units of B)

Now, we want to minimize \( z \), which represents the number of units of product C. To do this, we can substitute the minimum required values for \( x \) and \( y \) into the total production equation.

Using the minimum values:
- Take \( x = 20 \)
- Take \( y = 30 \)

Substituting these values into the total production requirement gives:
\[
20 + 30 + z = 200
\]
\[
50 + z = 200
\]
Now, solve for \( z \):
\[
z = 200 - 50 = 150
\]

Thus, the minimum number of units of product C that must be produced is \( \boxed{150} \).