The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model. P(x) = 230 + 40x - 0.5x2 What expenditure for advertising will yield a maximum profit?
A) 40
B) 0.5
C) 230
D) 20

Given that The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model.

[tex]P(x) = 230 + 40x - 0.5x^2[/tex]

We can use derivative test to find maximum

Differentiate two times the profit funciton

[tex]P'(x) = 40-x\\P"(x) = -1[/tex]

Equate I derivative to 0

we get

[tex]x=40[/tex]

II derivative is alrways negative

Hence profit is maximum when x=40

Option A is right

The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model. P(x) = 230 + 40x - 0.5x2 What expenditure for advertising will yield a maximum profit? A) 40 B) 0.5 C) 230 D) 20

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The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model. P(x) = 230 + 40x - 0.5x2 What expenditure for advertising will yield a maximum profit?
A) 40
B) 0.5
C) 230
D) 20