Question 912653
11 thousand units is correct, but 345 thousand dollars is not.


P(x)=-x^2+22x-18


P(11)=-(11)^2+22(11)-18 ... everywhere you see an 'x', replace it with 11


P(11)=-121+242-18


P(11)=103


So the correct max profit is <font color="red">103 thousand dollars</font>


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We want to solve P(x) >= 40


If we graph P(x)=-x^2+22x-18 (in <font color="green">green</font>) and the horizontal line y = 40 (in <font color="blue">blue</font>), we get this


{{{drawing(500,500,-10,30,-10,120,
  grid(0),
  graph(500,500,-10,30,-10,120,0,-x^2+22x-18,40)
)}}}


using the graphing calculator intersect feature, or the quadratic formula, we see that the solutions to -x^2+22x-18 = 40 are x = 3.062746067, x = 18.93725393. They are rough approximations


Round up to the nearest unit to get x = 3 or x = 19


So you need to produce more than <font color="red">3 thousand units</font>, but less than <font color="red">19 thousand units</font> to have a profit of at least 40 thousand.



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Thanks,


Jim