Question 1042820
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Problem 1



Plug in x = 20



{{{P(x)=-2x^2+100x-980}}}



{{{P(20)=-2(20)^2+100(20)-980}}} Replace every x with 20. Now evaluate/simplify.



{{{P(20)=-2(400)+100(20)-980}}}



{{{P(20)=-800+2000-980}}}



{{{P(20)=1200-980}}}



{{{P(20)=220}}}



When 20 frames are manufactured, the weekly profit is $220



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Problem 2



In the case of y = -2x^2+100x-980, it is of the form y = ax^2 + bx + c where
a = -2
b = 100
c = -980
We will plug a = -2 and b = 100 into the formula x = -b/(2a) to find the x coordinate of the vertex.



{{{x = -b/(2a)}}}



{{{x = -b/(2*(-2))}}} Plug in a = -2



{{{x = -100/(2*(-2))}}} Plug in b = 100



{{{x = -100/(-4)}}}



{{{x = 25}}}



This means that the max weekly profit occurs when 25 frames are made.



Plug x = 25 into the P(x) function to find the y coordinate of the vertex.



{{{P(x)=-2x^2+100x-980}}}



{{{P(25)=-2(25)^2+100(25)-980}}} Replace every x with 25. Now evaluate/simplify.



{{{P(25)=-2(625)+100(25)-980}}}



{{{P(25)=-1250+2500-980}}}



{{{P(25)=1250-980}}}



{{{P(25)=270}}}



The max weekly profit is $270
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