Mat222 Week 4 Assignment Essay Example
One of the lessons of this week was related to quadratic functions. Quadratic equations in the real world can be utilized for foretelling the results of a race based on previous statistics.
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 = −25x2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit?
p = -25x2 + 300x quadratic equation
Therefore you can find the max profit by finding the value of x of the axis of symmetry and find the vertex with that:
Axis of symmetry formula: x = -b/ (2a)
In equation; p = -25x2 + 300x a = -25 b = 300
x = -300/ (2 X -25)
x = -300/ -50
x = +6 clerks will maximize the profit
To find the max profit, substitute 6 for x in the original equation: p = -25(6^2) + 300(6)
p = -25(36) + 1800
p = -900 + 1800
p = $900 is the actual profit
A profit/clerk graph will look like this:
:
Notice the max occurs when x = 6 clerks which is the axis of symmetry and the vertex is the max profit of 900
Say for instance the profit coming in was at its lowest, that’s where the manager would step in to increase the profit. He would do this by looking at the profit when it was at its maximum and figure out what made it decrease and how he can bring it back to its maximum. He could hire more clerks to work certain shifts or to work in the store at all times. In other words saying that using this method would help the manager know the maximum or minimum amount of clerks needed to bring the profit to its
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 = −25x2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit?
p = -25x2 + 300x quadratic equation
Therefore you can find the max profit by finding the value of x of the axis of symmetry and find the vertex with that:
Axis of symmetry formula: x = -b/ (2a)
In equation; p = -25x2 + 300x a = -25 b = 300
x = -300/ (2 X -25)
x = -300/ -50
x = +6 clerks will maximize the profit
To find the max profit, substitute 6 for x in the original equation: p = -25(6^2) + 300(6)
p = -25(36) + 1800
p = -900 + 1800
p = $900 is the actual profit
A profit/clerk graph will look like this:
:
Notice the max occurs when x = 6 clerks which is the axis of symmetry and the vertex is the max profit of 900
Say for instance the profit coming in was at its lowest, that’s where the manager would step in to increase the profit. He would do this by looking at the profit when it was at its maximum and figure out what made it decrease and how he can bring it back to its maximum. He could hire more clerks to work certain shifts or to work in the store at all times. In other words saying that using this method would help the manager know the maximum or minimum amount of clerks needed to bring the profit to its