Solve the problem.
-The profit that a vendor makes per day by selling x pretzels is given by the function $$P ( x ) = - 0.004 x ^ { 2 } + 2.8 x - 250$$ Find the number of pretzels that must be sold to maximize profit.
A)240 pretzels
B)350 pretzels
C)1.4 pretzels
D)700 pretzels

Question

Quizplus · Accepted Answer

The function is a quadratic equation in the form of $ ax^2 + bx + c $, where $ a = -0.004 $, $ b = 2.8 $, and $ c = -250 $. The maximum profit occurs at the vertex of the parabola, which is given by $ x = -\frac{b}{2a} $. Substituting the values, $ x = -\frac{2.8}{2 \times -0.004} = 350 $.

Solve the Problem P(x)=−0.004x2+2.8x−250P ( x ) = - 0.004 x ^ { 2 } + 2.8 x - 250P(x)=−0.004x2+2.8x−250

Solve the Problem $P ( x ) = - 0.004 x ^ { 2 } + 2.8 x - 250$