MHB Help me with profit maximizing level of output

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To determine the profit-maximizing level of output for Happy Planet drinks, the price function is given as p=10-0.005x, with a variable cost of $2.50 per drink and a fixed monthly cost of $1000. Profit is calculated as total revenue minus total cost, and maximum profit occurs when marginal profit is zero. For Richard Simmons exercise videos, total revenue is represented by TR=21x-0.5x^2 and total cost by TC=5x+3, with maximum profit needing to be calculated similarly. Participants in the discussion emphasize the importance of understanding revenue, total cost, and profit calculations to solve these problems effectively.
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I really do not understand what my instructor taught about profit maximizing and profit earned at maximum...so please tell me how to solve them. Thank you very much!

Happy Planet drinks price change as the quantity sold changes. In particular \(p=10-0.005x\).

The total cost to produce the drinks are \(\$2.50\) per drink.

Their production factory costs \(\$1000\) per month.

What is the profit maximizing level of output?

Richard Simmons exercise videos have a \(TR=21x-0.5x^2\) and \(TC=5x+3\).
What is the profit earned at maximum?
 
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Re: help me with profit maximizing level of output

Hello foskel,

A few things we need to know are:
  • Revenue is price per unit times units sold
  • Total cost is cost per unit times units sold to which we add fixed costs
  • Profit is revenue minus total cost
  • Maximum profit occurs where marginal profit is zero

Can you use this information to solve the problems? If you still need guidance, please feel free to let us know and we will gladly offer further help, but I want to give you a chance to works these yourself first.
 
Re: help me with profit maximizing level of output

foskel said:
I really do not understand what my instructor taught about profit maximizing and profit earned at maximum...so please tell me how to solve them. Thank you very much!

Happy Planet drinks price change as the quantity sold changes. In particular p=10-0.005x.

The total cost to produce the drinks are $2.50 per drink.

Their production factory costs $1000 per month.

What is the profit maximizing level of output?

Richard Simmons exercise videos have a TR=21x-0.5 and TC=5x+3.
What is the profit earned at maximum?


Hello foskel,
just a tips don't use latex code when you write sentence. I honestly tried it as well and I don't know if you can get space when you write sentence on latex but right now there is none space in each words.
 
Last edited:
Re: help me with profit maximizing level of output

Petrus said:
Hello foskel,
just a tips don't use latex code when you write sentence. I honestly tried it as well and I don't know if you can get space when you write sentence on latex but right now there is none space in each words.

I think it was accidental, and because of the dollar signs. Use backslash + dollar to escape dollar signs:

Code:
$250 and this will be munched up by LaTeX ... $500
Code:
\$250 and this will work fine ... \$500

$250 and this will be munched up by LaTeX ... $500

\$250 and this will work fine ... \$500
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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