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The total cost of producting X items per day ₹(X^2÷4+35X+25)and the price per items at which they may be sold is ₹(50-X÷2).find the daily output to maximize the profit

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  1. profit is revenue - cost
    revenue is price * quantity
    So, the profit is
    x(50 - x/2) - (x^2/4 + 35x + 25) = 1/4 (-3x^2 + 60x - 100)
    As with all parabolas, the vertex is at
    x = -b/2a = -60/-6 = 10

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