The total profit P(x) (in thousands of dollars) from a sale of x thousand units

Question

The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = ln (- x3 + 3x2 + 105x + 1) (0 x 10). a) Find the number of units that should be sold in order to maximize the total profit. b) What is the maximum profit? The number of units that should be sold in order to maximize the total profit is . (Simplify your answer.) The maximum profit is approximately S . (Do not round until the final answer. Then round to the nearest dollar as needed.)

Explanation / Answer

P'(x)=0 ==>(-3x^2+6x+105)/(-x^3+3x^2+105x+1)=0 ==>x^2-2x+35=0 ==>x=7 so 7*1000=7000 units must be sold maximum profit=ln(-7^3 +3*7^2+105*7+1) 1000$ =6.837.2*1000 =6837.2$

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