Question

18) The profit that the vendor makes per day by selling x pretzels is given by the function

P(x) = -0.004x2 + 2.8x - 100. Find the number of pretzels that must be sold to maximize profit.
A) 390 pretzels
B) 350 pretzels
C) 700 pretzels
D) 1.4 pretzels

Answer 1

• B) 350 pretzels

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Given

• Function P(x) = - 0.004x² + 2.8x - 100

To find

• The value of x, which makes the P(x) maximum

Solution

This is a quadratic function and it can get maximum at vertex.

The x-coordinate of the vertex is determined by x = - b/(2a).

We have:

• a = - 0.004 and
• b = 2.8

Find the value of x:

• x = - 2.8 / (2* (-0.004)) = 350

Correct choice is B.