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 maximum profit which can manufacturer earn?

Options

A. Rs 240250
B. Rs 480500
C. Rs 680250
D. Rs 240250

Answer

A

Explanation

Rearranging the given equation we have
`P(x) = -10x^(2) +3500x - 66000`
` = -10 (x^(2) -350x +6600)`
`= -10 [(x-175)^(2) -30625 +6600]`
`=-10 [(x-175)^(2) -24025]`
`= -10(x-175)^(2)+240250`
From above equation it is clear that maximum value of P(x) is 240250.
Thus (a) is correct option.