An event management company charges ₹ …
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Preeti Dabral 1 year, 2 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.
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