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To determine the **minimum number of cucumbers** that can be planted based on the given conditions, we need to interpret both conditions carefully:

1. **Condition (i)**: The maximum number of cucumbers and tomatoes combined is 300.
   
   Let the number of cucumbers be denoted by \( C \) and the number of tomatoes be \( T \).
   Therefore, \( C + T \leq 300 \).

2. **Condition (ii)**: The number of tomatoes is less than 100.

   So, \( T < 100 \).

### Finding the minimum number of cucumbers
To minimize the number of cucumbers, we need to maximize the number of tomatoes. From condition (ii), the maximum number of tomatoes is less than 100, so the maximum value \( T \) can take is 99.

Now, substitute \( T = 99 \) into the first condition:
\[
C + 99 \leq 300
\]
\[
C \leq 300 - 99
\]
\[
C \leq 201
\]
Thus, when \( T = 99 \), the maximum possible number of cucumbers is 201. To minimize the number of cucumbers, \( T \) should be maximized, so the **minimum number of cucumbers** is **201**.

### Explanation for item 5ci
The answer is based on maximizing the number of tomatoes (99), which allows the minimum number of cucumbers to be 201, as the sum of cucumbers and tomatoes cannot exceed 300.

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Would you like further clarification on this? Here are some additional related questions:

1. What happens if the number of tomatoes is less than 99?
2. How would the solution change if the maximum number of cucumbers and tomatoes was increased to 400?
3. What if there was a minimum requirement for cucumbers?
4. Can you calculate the number of cucumbers if there were 50 tomatoes?
5. What happens if both the cucumbers and tomatoes are equally limited to less than 150?

**Tip**: When maximizing or minimizing a number, always check if any constraints limit the other variable!

Based on the planting conditions below, what is the minimum number of cucumbers that can be planted? The maximum number of cucumbers and tomatoes is 300, and the number of tomatoes is less than 100.

Discover how to minimize the number of cucumbers that can be planted when the maximum combined number of cucumbers and tomatoes is 300, and the number of tomatoes must be less than 100. This problem covers algebraic inequalities and optimization techniques.

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