An event management company charges ₹ …

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An event management company charges ₹ 4,800 per guest, for a bulk booking for 100 guests. In addition, it offers a discount of ₹ 200 for each group of 10 guests over and above 100 guest booking. What is the number of guests that will maximise the amount of money the company receives on a booking? What is the maximum profit on such booking?

Posted by Tanushri Bhayani 1 year, 8 months ago

CBSE > Class 12 > Applied Maths

2 answers

Preeti Dabral 1 year, 8 months ago

Let the number of guests be x

If x > 100, then the amount received by the company will be-

{4800 - 200/10(x - 100)}x

Now, we need to maximize this amount so let us differentiate with respect to x as follows-

P = 4800x - 20(x - 100)x

P = 4800x - 20x² + 2000x

P = 6800x - 20x²

dP/dx = 6800 - 40x

differentiating again-

d²P/dx² = -40

As d²P/dx² > 0, the maximum value will occur at dP/dx = 0

⇒ 6800 - 40x = 0

40x = 6800

x = 6800/40

x = 170

Now, the amount received will be = 6800(170) - 20(170)²

= 1156000 - 578000

= 578000

Thus, the maximum amount that the company will receive is 5,78,000 when the number of guests are 170.

1Thank You

Tanushri Bhayani 1 year, 8 months ago

Thank you bro

0Thank You

ANSWER

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CBSE > Class 12 > Applied Maths