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1. The problem statement, all variables and given/known data

Note: This problem comprises many parts, but I will just skip to the last one, since it's the one I'm struggling to answer!

An economist producing x thousand items attempts to model a profit function as a quadratic model P(x) = ax²+bx+cthousanddollars.

Given info: a=t, b=3-5t, c=5+4t = possible solutions for the system

part c asks us to find the "actual profit function" when the profit for producing 2500 items is 19,750 dollars (Note: 19750 becomes 19.75 when we plug into the function)...

Then part d asks us what is the max profit to be made and what level of production is needed to acheive it?

2. Relevant equations

3. The attempt at a solution

After substitution, the function for part c is as follows:

p(x)= (-29/9)x²+(172/9)x-(71/9) thousand dollars

such that 19.75= (-29/9)x²+(172/9)x-(71/9) thousand dollars

I'm guessing we have to use this formula to answer part d...I have solved x, where, in this case, x=0.44 or 5.48

Yet, I don't think these x-values will help me solve part d?!

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# Homework Help: Matrices & word problem

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