SOLUTION: ABC Company manufactures picture frames. The weekly profit function is given by P(x)=-2x^2+100x-980 1. What is the profit/loss when 20 frames are manufactured? 2. Find the quan

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: ABC Company manufactures picture frames. The weekly profit function is given by P(x)=-2x^2+100x-980 1. What is the profit/loss when 20 frames are manufactured? 2. Find the quan      Log On

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Question 1042820: ABC Company manufactures picture frames. The weekly profit function is given by
P(x)=-2x^2+100x-980
1. What is the profit/loss when 20 frames are manufactured?
2. Find the quantity that maximizes weekly profit and the maximum weekly profit.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Problem 1


Plug in x = 20


P%28x%29=-2x%5E2%2B100x-980


P%2820%29=-2%2820%29%5E2%2B100%2820%29-980 Replace every x with 20. Now evaluate/simplify.


P%2820%29=-2%28400%29%2B100%2820%29-980


P%2820%29=-800%2B2000-980


P%2820%29=1200-980


P%2820%29=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%2F%282a%29


x+=+-b%2F%282%2A%28-2%29%29 Plug in a = -2


x+=+-100%2F%282%2A%28-2%29%29 Plug in b = 100


x+=+-100%2F%28-4%29


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%28x%29=-2x%5E2%2B100x-980


P%2825%29=-2%2825%29%5E2%2B100%2825%29-980 Replace every x with 25. Now evaluate/simplify.


P%2825%29=-2%28625%29%2B100%2825%29-980


P%2825%29=-1250%2B2500-980


P%2825%29=1250-980


P%2825%29=270


The max weekly profit is $270