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
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