MATH: Carissa needs to rent a car while on vacation. The rental company charges $19.95, plus 18 cents for each mile driven. If C
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Answer:
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
In this question:
Permutations of four letters from a set of 12 letters. So
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Continuing from the setup in the question linked above (and using the same symbols/variables), we have
The next part of the question asks to maximize this result - our target function which we'll call
- subject to 
.
We can see that
is quadratic in 
, so let's complete the square.
Since
are non-negative, it stands to reason that the total product will be maximized if 
vanishes because 
is a parabola with its vertex (a maximum) at (5, 25). Setting 
, it's clear that the maximum of will then be attained when are largest, so the largest flux will be attained at 
, which gives a flux of 10,800.
The next part of the question asks to maximize this result - our target function which we'll call
We can see that
Since