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# Application of Algebraic Polynomials in Cost Accountancy

MP3 players example

The profit in millions of dollars for an MP3 player can be done with the polynomial P=-4x^3 + 12X^2 + 16X. X represents the number of MP3 players produced annually. The company currently produces 3 million MP3 players and makes a profit of \$ 48,000,000. To figure out the least amount of MP3 players the company can produce and still make the same profit we need to solve for P.

Step 1
Set P=48 This represents the total profit. 48=-4X^3 + 12X^2 + 16X

Step 2 subtract the 48 from 48 and from the end of the equation, like this 48=-4X^3 + 12X^2 + 16X - 48
-48
Step 3 Than you factor by using the Greatest Common Factor as show below.

-4X^2(X-3) + 16 (X-3) Notice how it is now a binomial, which means two terms. It was previously a Trinomial.

Step 5 Multiply the variables in each Binomial separately and set them equal to 0.If necessary, you might need to divide like the Binomial 2

So -4X^2(X-3) turns to 4X^2+16=0 and 16(X-3) 16X/-48 than   X-3=0

Step 6
Subtract 16 from Equation 1 and  add 3 to Equation 2 to get the results shown below
4X^2=-16 and X=3

Step 7 Reduce the terms in equation 1
16 can be reduced to 4, because 4*4=16, while 4x^2 can be reduced to X^2.

Step 8 solve 4=X^2. The answer is 2 or 2 million MP3s can be manufactured make the same profit of 4 3 million.

Step 9 Double check
48=-4(2)^2+12(2)^2+12(2)

The company can produce 2 Million MP3s and still make the same profit as producing 3 million MP3s. The reason for this is that perhaps variable costs doesn't change if they produce 1 million less MP3s. It could be that their production facilities got more efficient at producing the MP3s. It now takes less time and money to make the MP3s, so they company can afford to produce 2 million units and still earn the same profit as making 3 million units.

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