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
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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) (Show Source): You can put this solution on YOUR website!
Problem 1
Plug in x = 20
Replace every x with 20. Now evaluate/simplify.
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.
Plug in a = -2
Plug in b = 100
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.
Replace every x with 25. Now evaluate/simplify.
The max weekly profit is $270
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