A company produces products A and B. Product A earns Rs. 30 and uses 2 labour hours, while product B earns Rs. 20 and uses 1 labour hour. If at most 100 labour hours are available, which objective function represents profit maximization?
Correct answer: D. Maximize Z = 30A + 20B
- A. Minimize Z = 2A + B
- B. Maximize Z = 2A + B
- C. Minimize Z = 30A + 20B
- D. Maximize Z = 30A + 20B
Explanation
The objective function contains the profit contribution of each product, so it is 30A + 20B and must be maximized. The labour usage, 2A + B, belongs in the resource constraint rather than the objective.
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Linear programming models the maximum or minimum of an objective function subject to linear constraints. Questions involve translating word conditions into inequalities, drawing the feasible region, identifying corner points and evaluating the objective function, including cases involving non-negativity restrictions and redundant constraints.
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