Question

A manufacturer can sell 'x' items at the rate of (330-x) each. The cost of producing x items is rupees x​​​​​​2 + 10x + 12. How many items must be sold so that his profit is maximum?

Answer 1

we have the formula of the income money for x items:
x*(330-x)
and we have the formula for the cost:
x^2+10*x+12

we want to maximize the profit
max (income - cost)

max(330*x-x^2-x^2-10*x-12)
= max(-2*x^2+320*x-12)

parabola.... max point is x=-b/2*a
=-320/-4 = 80