Linear Programming · Class 12 · CBSE · Science Mathematics
A bakery produces cakes and pastries. Each cake requires 2 kg of flour and 1 hour of labour, while each pastry requires 1 kg of flour and 2 hours of…
Practice question from Linear Programming (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · Subjective · Q-BBC65C
A bakery produces cakes and pastries. Each cake requires 2 kg of flour and 1 hour of labour, while each pastry requires 1 kg of flour and 2 hours of labour. The bakery has 40 kg of flour and 30 labour hours available. It can sell at most 15 cakes and 20 pastries. The profit is Rs 60 per cake and Rs 50 per pastry. Formulate the corresponding linear programming problem.
Solution
Let x and y represent the numbers of cakes and pastries. The flour and labour limitations give 2x + y ≤ 40 and x + 2y ≤ 30, while the sales limits give x ≤ 15 and y ≤ 20. The profit function is Z = 60x + 50y, which is to be maximised.
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