Haven't found the Essay You Want?
For Only $12.90/page

Real World Quadratic Functions Essay

Maximum profit. A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P = ? 25×2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit? In order to find the point at which profit is maximized, I must find the critical points of the first derivative of the equation. Coefficient of x^2 is negative, so the maximum value of P will be found at the parabola’s vertex.

I also know that it has to be symmetric, so the average of or mid-point between the roots of the function will give me the x value of the vertex. The x-coordinate of the vertex is given by: x = b/2·a, and so the maximum value of P will be found at x = b/2·a My equation is already in the standard form: P=ax^2+bx+c, p = -25×2 + 300x quadratic equation Therefore I can find the max profit by finding the value of x of the axis of symmetry and find the vertex with that: this is a quadratic equation with a negative coefficient of x^2, so I know that the max is on the axis of symmetry.

The formula for the axis of symmetry; x = -b/ (2a), in this equation a = -25, b = 300 X = – 300 / 2 · (-25) I will Simplify the equation x = -300/ -50 Divide x = 6 The basic shape of the graph in this equation of a parabola that opens downwards (coefficient of x^2 is negative) so the maximum value of P will be found at the parabola’s vertex. The parabola will cross the x axis at 0 and 6.

To maximize profits, the manager should employ 6 clerks. The maximum profit can be found by substituting 6 for x in the original equation for P. P = -25 · (6)^2 + 300 · (6) Plug in 6 P = -25 · (36) + 1800 Multiply and add P = -900 + 1800 Add the equation P = 900 Maximum profit is 900 The graph represents the max occurs when x = 6 clerks which is the axis of symmetry and the vertex is the max profit of 900.

In conclusion the graph shows that there will be a maximum profit 900 in profit made with having 6 clerks. What I learned is that the graph of the profit function is a convex down parabola because of the negative lead coefficient. Hence, understanding that the vertex of the parabola is a maximum. All that was needed to solve the equation was finding the X coordinate of the vertex. The coordinates of the vertex y-coordinate of vertex will give me the maximum value

Essay Topics:

Sorry, but copying text is forbidden on this website. If you need this or any other sample, we can send it to you via email. Please, specify your valid email address

We can't stand spam as much as you do No, thanks. I prefer suffering on my own