To formulate the objective function for this problem, we need to express the goal, which is to **maximize the revenue** from selling the pineapples. Let's define the variables and constraints first:

### Variables:
- Let $ P $ be the number of pineapples produced per week.
- Let $ N $ be the number of boxes sold.
- Let $ S $ be the price per box, which is $10.
- Let $ T $ be the number of weeks in a month (4 weeks).
- Let $ R $ be the total revenue.

### Constraints:
1. Each box contains 10 pineapples, so $ N = \frac{P \times T}{10} $.
2. The farm produces 200 pineapples per week, so $ P = 200 $.
3. The total number of pineapples produced in a month: $ P \times T = 200 \times 4 = 800 $ pineapples.
4. Each box sells for $10, so $ S = 10 $.

### Objective Function:
The objective is to maximize the revenue $ R $, which is given by:

\[
R = N \times S
\]

Substituting the constraints:

\[
R = \left(\frac{P \times T}{10}\right) \times S
\]

Since $ P = 200 $, $ T = 4 $, and $ S = 10 $:

\[
R = \left(\frac{200 \times 4}{10}\right) \times 10 = \left(\frac{800}{10}\right) \times 10 = 80 \times 10 = 800
\]

Thus, the objective function is:

\[
R = 80 \times S = 80 \times 10 = 800
\]

### Final Objective Function:
\[ R = 800 \text{ dollars per month} \]

This function represents the total revenue generated in a month under the given constraints.

Would you like more details, or do you have any further questions?

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Here are 5 additional questions related to this topic:
1. How would the objective function change if the farm increased production to 250 pineapples per week?
2. What if the price per box was variable? How would you express the objective function?
3. How would introducing a cost for storage affect the objective function?
4. Can you formulate an objective function if the farm wants to maximize profit rather than revenue?
5. How would the objective function change if there was a limit on the number of boxes that could be sold each month?

**Tip:** When formulating objective functions, clearly identify the decision variables and constraints to ensure accurate modeling.

Learn how to formulate an objective function to maximize revenue from pineapple sales. This problem involves linear programming concepts, objective functions, and constraints. Explore the revenue formula and constraints involved in maximizing revenue from selling pineapples.

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