Question

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

Answer 1

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

$P(x)=-0.004x^2+2.8x-350$

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

$P'(x)=-0.008x+2.8$

For critical points, we get that

$P'(x)=0\\\\-0.008x+2.8=0\\\\-0.008x=-2.8\\\\x=\dfrac{2.8}{0.008}\\\\x=350$

Now, we will check for maximum profit.

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

$p''(x)=-0.008$

So, it will give maximum profit.

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

Therefore, Option 'c' is correct.