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How many units should be sold so that a company can make maximum profit if the profit function for x units is given by p(x) = 25 + 64x - x2
- a)16 units
- b)32 units
- c)8 units
- d)64 units
Correct answer is option 'B'. Can you explain this answer?
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How many units should be sold so that a company can make maximum profi...
Solution:
To find the maximum profit, we need to differentiate the profit function with respect to x and equate it to zero.
p(x) = 25x - 64x^2 + x^2
p'(x) = 25 - 128x + 2x
Setting p'(x) = 0, we get
2x - 128x + 25 = 0
Simplifying the above equation, we get
x = 16 units or 8 units
We need to check which of the above values of x gives us the maximum profit. To do this, we can differentiate the profit function twice and check the sign of the second derivative.
p''(x) = -128 + 2 = -126
Since p''(x) is negative, we can conclude that x = 16 units gives us the maximum profit.
Therefore, the correct answer is option B, 32 units.
To find the maximum profit, we need to differentiate the profit function with respect to x and equate it to zero.
p(x) = 25x - 64x^2 + x^2
p'(x) = 25 - 128x + 2x
Setting p'(x) = 0, we get
2x - 128x + 25 = 0
Simplifying the above equation, we get
x = 16 units or 8 units
We need to check which of the above values of x gives us the maximum profit. To do this, we can differentiate the profit function twice and check the sign of the second derivative.
p''(x) = -128 + 2 = -126
Since p''(x) is negative, we can conclude that x = 16 units gives us the maximum profit.
Therefore, the correct answer is option B, 32 units.
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How many units should be sold so that a company can make maximum profit if the profit function for x units is given byp(x) = 25 + 64x - x2a)16 unitsb)32 unitsc)8 unitsd)64 unitsCorrect answer is option 'B'. Can you explain this answer?
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