Let's take a look at an example
The setup cost for the project to develop a new tank design is 50 thousand dollars.
The development cost is a function of time. In other words, the cost increases
with time. From previous contracts, the cost function is estimated to be
where t is the time measured in working days. Suppose that a cost analyst
has 650 thousand dollars allocated for the project, and he/she wants to know how long
before he/she needs to allocate more resources to complete the project?
Let's consider a solution
The total cost for the tank is equal to the sum of the initial cost and the
development cost.
If $650 thousand has been given, we want to know how much
time before more resources needs to be allocated?
If we move 650 to the left of the equal sign, this is what we have
To solve the equation above, we just factor the terms as follow:
The equation yields two answers: t = -20 and t = 30. Since negative time has
no physical meaning, t = 30 is the only valid solution
It takes 30 working days before the cost analyst needs to allocate
more resources to fund the project.
A few simple facts that you should know
Did you know that the above example has a quadratic equation?
What is a quadratic equation anyway?
A Quadratic Equation is a polynomial equation in which the highest power of
the unknown variable is 2.
The most common form of a quadratic equation is an equation where the right hand
side is usually set to zero and that the highest exponent of any unknown
variable is 2.
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