Real World Quadratic Functions
Quiz 1. Maximum profit of a given a chain store has the main office is that the daily profit P is correlated with the number of clerks working that day, x, according to the equation p=-25x^2+300x. What is the number of clerks who will maximize the profit, and what is the maximum possible profit?
Solution
The quadratic equation provided (i.e.| p = -25x^2 + 300x) is to help us can find the number of clerks that if added will maximize the profit and find also the maximum profit that these clerks will bring. This can be done by finding the x value. To find the x value we need to plot a graph of the axis of symmetry which will help to find its.
The number of clerks
x = -b/(2a) should be the formula that the Axis of symmetry provides
when we substitute these two numbers from the equation:
p = -25x^2 + 300x
b = 300 while a = -25
x = -300/(2*-25)
x = -300/-50
x = 6
This is to mean that the number of clerks who need to be added to maximize the profits are 6
What is the maximum profit that will be produced by the 6 clerks?
In order to get the maximum profit that will be produced by the 6 clerks, we need to substitute 6 for x from the original equation:
p = -25(62) + 300*6
p = -25*36 + 1800
p = -900 + 1800
p = $900 will now be the maximum profit delivered by the 6 clerks.
The graph
the clerk/profit graph will look like this:
According to this graph, there will be any profits made when the number of clerks working are zero. The maximum profit will only be made when 6 clerks are working.
Keep in mind that the maximum profit are made when x = 6 clerks which is the axis of symmetry and the peak is the max profit of $900.
Quiz 2. Discuss how and why this is important for managers to know, and explain what could happen if the ideal conditions were not met.
There are several reasons why managers in any company need to know what needs to be done to maximize profits. You will agree with me that any company as a going concern does not exist in a void. Beyond any company’s interconnection of resources, it needs to guidelines in terms of where the company will go according to the manager. In this case, the manager needs to also decide how he or she would wish his organization to go in order to develop. One of the reasons why the main office had to inform the manager on the number of required clerks that are required to maximize the company’s income is because they wanted work towards their strategic feature of the company. The company needs to do everything possible to relate to its mission and perhaps an idealistic statement regarding the future of the company (Ziauddin, S., Jerry, R., and Borin Van Loon, 1999).
. If the main office did not inform the manager on what needs to be done to maximize the profits of the company, mostly probably, the company's income would have remained steady or even depreciate. The second thing that is mostly likely to happen is the company is likely to collapse, as well. This is because these people in the main offices are very aware of what is happening in the actual field and their recommendations need to be well addressed (Ziauddin, S., Jerry, R., and Borin Van Loon, 1999).
References
Ziauddin, S., Jerry, R., and Borin Van Loon. (1999). Introducing Mathematics. Totem Books.
