Question

A company makes digital cameras. The company estimates that their profit in millions of dollars can...

A company makes digital cameras. The company estimates that their profit in millions of dollars can be given by the function P (x) = −0.02x3 + 0.01x2 + 1.2x − 1.1 where x is the amount in hundred thousands spent on advertising. How much should they spend on advertising if they wish the profit to be 2 million dollars?
Math   Precalculus   
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Answer #1

Given, P(x) = -0.02x³ + 0.01x² + 1.2x - 1.1

where, P(x) is profit in million dollars and x is amount in hundred thousands spent on advertisement.

Here, P(x)=2

∴2= - 0.02x³ + 0.01x² + 1.2x - 1.1

=>200= -2x³ + x² + 120x - 110

=>2x³ - x² - 120x + 310=0

=>x= -8.588, 2.9316 or 6.1564

but x cannot be negative.

∴x =2.9316 or 6.1564

The company should spend 2.9316 hundred thousands or 6.1564 hundred thousands if they wish the profit to be 2 million dollars.

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