Help me with profit maximizing level of output

[foskel]

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?
​

 

[MarkFL]

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.

 

[Petrus]

Re: help me with profit maximizing level of output

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.

 

[Nono713]

Re: help me with profit maximizing level of output

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:

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

\$250 and this will work fine ... \$500

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

\$250 and this will work fine ... \$500

 

[CellCoree]

Hello,

Profit maximizing level of output refers to the quantity of a product or service that a company should produce in order to maximize their profits. This can be calculated by finding the point where marginal revenue (MR) equals marginal cost (MC). In other words, the level of output where the additional revenue gained from producing one more unit is equal to the additional cost of producing that unit.

In the case of Happy Planet drinks, the profit maximizing level of output can be calculated by setting MR equal to MC:

MR = p = 10 - 0.005x
MC = $2.50 + $1000/month = $2.50 + $1000/30 days = $2.50 + $33.33 = $35.83

Setting MR = MC:

10 - 0.005x = $35.83
- 0.005x = $25.83
x = $25.83/-0.005
x = 5166

Therefore, the profit maximizing level of output for Happy Planet drinks is 5166 drinks per month.

To calculate the profit earned at maximum, we need to find the difference between total revenue (TR) and total cost (TC) at the profit maximizing level of output:

TR = p * x = (10 - 0.005x) * x = $10x - 0.005x^2
TC = $2.50x + $1000 = $2.50 * 5166 + $1000 = $12,915
Profit = TR - TC = ($10x - 0.005x^2) - ($2.50x + $1000) = $7.50x - 0.005x^2 - $1000

Substituting x = 5166:

Profit = ($7.50 * 5166) - (0.005 * 5166^2) - $1000 = $38,745 - $133,932 - $1000 = -$95,187

Therefore, the profit earned at maximum for Happy Planet drinks is -$95,187. This means that the company is making a loss at the profit maximizing level of output.

For the Richard Simmons exercise videos, the profit maximizing level of output can be calculated in the same way as above, by setting MR equal to MC:

MR = TR' = 21 - 1x = 21 - 1