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The profit that the vendor makes per day by selling x pretzels is given by the function P(x) = -0.004 x^2 + 2.8x - 350. Find the number of pretzels that must be sold to maximize profit A) 325 pretzels B) 340 pretzels C) 350 pretzels

Respuesta :

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

[tex]P(x)=-0.004x^2+2.8x-350[/tex]

So, we will first derivative it w.r.t to x, we get that

[tex]P'(x)=-0.008x+2.8[/tex]

For critical points, we get that

[tex]P'(x)=0\\\\-0.008x+2.8=0\\\\-0.008x=-2.8\\\\x=\dfrac{2.8}{0.008}\\\\x=350[/tex]

Now, we will check for maximum profit.

So, we will find Second derivation and then put the value of x = 350 in it.

[tex]p''(x)=-0.008<0[/tex]

So, it will give maximum profit.

Hence, At 350 pretzels, there must be maximum profit.

Therefore, Option 'c' is correct.

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