Maximum profit: An barrels manufacturer can produce up to 300 barrels per day. The profit made from the sale of these barrels can be modelled by the function `P(x) = -10x^(2) +3500x -66000 ` where P(x) is the profit in rupees and x is the number of barrels made and sold.

Based on this model answer the following questions:
What is the break even point ? (Zero profit point is called break even)

Options

A. 10 barrels
B. 30 barrels
C. 20 barrels
D. 100 barrels

Answer

C

Explanation

At break-even point `P(x) = 0`, thus
`0 = -10x^(2) +3500x -66000`
`x^(2) +350x +6600=0`
`x^(2)-330x-20x+6600=0`
`x(x-330) -20(x+300)=0`
`(x-330) (x-20)=0`
`x=20, 330`
Thus, (c ) is correct option.