Question

A manufacturer can sell x items at a price of Rs(280-x) each.The cost of producing x items is Rs(x^2+40x+35).Find the number of items to be sold so that the manufacturer can make maximum profit.​

Answer 1

Step-by-step explanation:

A manufacturer can sell x items at a price of Rs(280-x) each.The cost of producing x items is Rs(x^2+40x+35).Find the number of items to be sold so that the manufacturer can make maximum profit.

Answer 2

Selling price of an item = Rs. (280 - x)

Let x be the number of items to be sol

:: Revenue = x( 280 - x )

= 280x - x2

Given total cost Rs. (x2 + 40x + 35)

Profit n = Revenue - total cost

= (280x - x2) - (x² + 40x + 35)

= -2x2 + 240x - 35

Diff. w.r.t.x.

dr

.. -2(2x) + 240 = 0 =

dx

= -4x + 240

Tt is maximum if,

- -4x + 240 = 0

- -4x = -240

» X = 60

Diff. again w.r.t.x.

dan dr

da?

dx

(-4x + 240)

= -4(1) + 0 = -4

dr

,2 dx?

-4 < 0

Profit is maximum when x = 60

:: Maximum profit when x = 60.

dn

dx

= 0

hope this helps you

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