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Answer:
Maximum profits are earned when x = 64 that is when 64 units are sold.
Maximum Profit = P(64) = 2,08,490.666667$
Step-by-step explanation:
We are given the following information:, where P(x) is the profit function.
We will use double derivative test to find maximum profit.
Differentiating P(x) with respect to x and equating to zero, we get,
Equating it to zero we get,
We use the quadratic formula to find the values of x:
, where a, b and c are coefficients of
respectively.
Putting these value we get x = -100, 64
Now, again differentiating
At x = 64,
Hence, maxima occurs at x = 64.
Therefore, maximum profits are earned when x = 64 that is when 64 units are sold.
Maximum Profit = P(64) = 2,08,490.666667$