A patient needs at least 36 units of vitamin supplement A, at least 36 units of vitamin supplement B and at least 24 units of vitamin supplement C. Local brand capsules contain 2 units of A, 3 units of B and 1 unit of C costs P15, while foreign brand capsules contain 6 units of A, 3 units of B and 6 units of C costs P25. How many capsules should the patient take each day in order to minimize the cost?

To minimize the cost, we need to consider the cost per unit of each vitamin supplement in each brand.

Let's start by calculating the cost per unit of each vitamin supplement for both the local and foreign brand capsules.

For the local brand capsules:
- Vitamin A: P15 / 2 units = P7.50 per unit
- Vitamin B: P15 / 3 units = P5 per unit
- Vitamin C: P15 / 1 unit = P15 per unit

For the foreign brand capsules:
- Vitamin A: P25 / 6 units ≈ P4.17 per unit
- Vitamin B: P25 / 3 units ≈ P8.33 per unit
- Vitamin C: P25 / 6 units ≈ P4.17 per unit

Now, let's calculate the number of capsules needed to meet the minimum requirements for each vitamin supplement.

For Vitamin A:
- For local brand capsules: 36 units / 2 units = 18 capsules
- For foreign brand capsules: 36 units / 6 units = 6 capsules

For Vitamin B:
- For local brand capsules: 36 units / 3 units = 12 capsules
- For foreign brand capsules: 36 units / 3 units = 12 capsules

For Vitamin C:
- For local brand capsules: 24 units / 1 unit = 24 capsules
- For foreign brand capsules: 24 units / 6 units = 4 capsules

To determine the minimum cost, we need to find the combination of capsules that fulfills the minimum requirements for each vitamin supplement while minimizing the cost per day.

Combination 1: Local brand capsules
- Vitamin A: 18 capsules
- Vitamin B: 12 capsules
- Vitamin C: 24 capsules

Total cost per day: (18 capsules × P7.50 per unit) + (12 capsules × P5 per unit) + (24 capsules × P15 per unit) = P135 + P60 + P360 = P555

Combination 2: Foreign brand capsules
- Vitamin A: 6 capsules
- Vitamin B: 12 capsules
- Vitamin C: 4 capsules

Total cost per day: (6 capsules × P4.17 per unit) + (12 capsules × P8.33 per unit) + (4 capsules × P4.17 per unit) = P25 + P99.96 + P16.68 = P141.64

Therefore, the patient should take 6 capsules of the foreign brand capsules. This combination will fulfill the minimum requirements for all vitamin supplements, while minimizing the cost per day.