The state wants to reduce the number of new drug initiates among 200,000 at‑risk youths by at least 20,000. Two intervention strategies are available:

Strategy A - Community education: costs ₦5,000 per person, reaches 10,000 youths, and reduces initiation among participants by 15%.
Strategy B - School‑based counselling: costs ₦8,000 per person, reaches 7,500 youths, and reduces initiation among participants by 25%.

Both strategies can be repeated in whole‑cycle units (i.e., each cycle reaches the same number of youths at the same cost and effect). Determine the combination of whole cycles of Strategies A and B that achieves the target reduction at the minimum total cost. State the number of cycles of each strategy, the total cost, and the total number of initiates prevented.

Question

The state wants to reduce the number of new drug initiates among 200,000 at‑risk youths by at least 20,000. Two intervention strategies are available:

Strategy A - Community education: costs ₦5,000 per person, reaches 10,000 youths, and reduces initiation among participants by 15%.
Strategy B - School‑based counselling: costs ₦8,000 per person, reaches 7,500 youths, and reduces initiation among participants by 25%.

Both strategies can be repeated in whole‑cycle units (i.e., each cycle reaches the same number of youths at the same cost and effect). Determine the combination of whole cycles of Strategies A and B that achieves the target reduction at the minimum total cost. State the number of cycles of each strategy, the total cost, and the total number of initiates prevented.

Accepted Answer

10 cycles of Strategy B and 1 cycle of Strategy A; total cost ₦650,000,000; 20,250 initiates prevented.

Waec Model Questions Vol1 2022 Civic Education Question 50

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