SOLUTION: It costs (20 + x) dollars to produce (x) number of products. If the products sell for (300 - 2x) dollars each, how many products should be produced each month to maximize profit?

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Question 119225This question is from textbook Algebra 2
: It costs (20 + x) dollars to produce (x) number of products. If the products sell for (300 - 2x) dollars each, how many products should be produced each month to maximize profit? This question is from textbook Algebra 2

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It costs (20 + x) dollars to produce (x) number of products. If the products sell for (300 - 2x) dollars each, how many products should be produced each month to maximize profit?
:
Organize what we know here:
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Cost for x items = (20+x)
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Revenue per item = (300-2x)
Revenue for x items = x(300-x)
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We know that profit is: Revenue - cost:
Write that equation where y = profit on x items
y = x(300-2x) - (20+x)
y = 300x - 2x^2 - 20 - x
y = 280x - 2x^2 - x
write it as a quadratic equation:
y = -2x^2 + 279x
:
Maximum profit occurs at the axis of symmetry, we can find that using
x = %28-b%29%2F%282a%29 where, in our equation, a = -2 and b = 279
x = %28-279%29%2F%282%2A-2%29
x = %28-279%29%2F%28-4%29
x = +69.75 items
We can't make .75 items, so say max profit when 70 items are made
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Did this make sense to you? Let me know.