The total profit Upper P (x )(in thousands of dollars) from the sale of x hundred thousand pillows is approximated by Upper P (x )equals negative x cubed plus 9 x squared plus 120 x minus 200, x greater than or equals 5. Find the number of hundred thousands of pillows that must be sold to maximize profit. Find the maximum profit.

10 hundred thousands of pillows must be sold to maximize the profit of 900 thousands dollars.

Step-by-step explanation:

We are given the following in the question:

Where P(x) is the profit in thousand of dollars and x is the hundred thousand pillows sold.

First, we differentiate P(x) with respect to x, to get,

Equating the first derivative to zero, we get,

Solving, with the help of quadratic formula, we get,

Again differentiation P(x), with respect to x, we get,

At x = 10

Thus,by double differentiation test maxima occurs at x = 10 for P(x).

Thus, 10 hundred thousands of pillows that must be sold to maximize profit.

Maximum Profit

Thus, the maximum profit is 900 thousands of dollars.

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