Question 169217
a.
Should be:
p = -x + 62
price
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b. YES!
R = xp
R = x(-x + 62)
R = -x^2 + 62x
revenue
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c. YES
b=300
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d. YES
C=6x+300 
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e. NO -- you have a "sign" problem.
profit = "revenue" - "cost"
P(x) = (-x^2 + 62x) - (6x+300)
P(x) = -x^2 + 62x - 6x - 300
P(x) = -x^2 + 56x - 300
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f. Since you had e. wrong, this is wrong
P(x) = -x^2 + 56x - 300
P(20) = -(20^2) + 56(20) - 300
P(20) = -(400) + 1120 - 300
P(20) = -700 + 1120
P(20) = $420
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g. Since you had e. wrong, this is wrong
P(x) = -x^2 + 56x - 300
P(25) = -(25^2) + 56(25) - 300
P(25) = -(625) + 1400 - 300
P(25) = -925 + 1400
P(25) = $475
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h. Since you had e. wrong, this is wrong
P(x) = -x^2 + 56x - 300
P(0) = -0^2 + 56(0) - 300
P(0) = -300
Even if you don't sell anything, you STILL have costs --  rent, insurance, and wages, etc.
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i.
Since the "profit" is increasing in part f. and g.
Try a larger number than 25 such as 35
P(x) = -x^2 + 56x - 300
P(35) = -(35^2) + 56(35) - 300
P(35) = -(1225) + 1960 - 300
P(35) = 435
Since it went DOWN from g. -- it's between 25 and 35...
The idea is to keep trying until you find the most profit...