A public agency must distribute a total budget of $120$ million naira among three programmes A, B and C. The allocation must satisfy:

1. Programme A receives at least $30\%$ of the total budget.
2. Programme B may not exceed $40\%$ of the total budget.
3. The amount for A and C must be in the ratio $3:2$.

The cost per outcome unit is $2$ million naira for A, $3$ million naira for B and $1$ million naira for C. The agency wishes to maximise the total number of outcome units produced, where the number of units from a programme equals the amount allocated divided by its cost per unit.

What allocation of the budget (in millions of naira) to A, B and C achieves the maximum total outcomes, and how many outcome units are obtained?

Question

A public agency must distribute a total budget of $120$ million naira among three programmes A, B and C. The allocation must satisfy:

1. Programme A receives at least $30\%$ of the total budget.
2. Programme B may not exceed $40\%$ of the total budget.
3. The amount for A and C must be in the ratio $3:2$.

The cost per outcome unit is $2$ million naira for A, $3$ million naira for B and $1$ million naira for C. The agency wishes to maximise the total number of outcome units produced, where the number of units from a programme equals the amount allocated divided by its cost per unit.

What allocation of the budget (in millions of naira) to A, B and C achieves the maximum total outcomes, and how many outcome units are obtained?

Accepted Answer

A = 72 million, B = 0 million, C = 48 million; total outcomes = 84 units.

Gce Model Questions Vol1 2017 Government Question 32

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