# Cost, revenue, profit: $24,000 fixed costs,$7/unit cost, $10/unit selling price #### sura0912 ##### New member Hi, can anyone help me with this problem. I dont really understand how it is to be done. A drink manufacturer has a monthly fixed cost of$24,000 and a production cost of $7 for each drink produced.The product sells for$10 per drink.

i. Derive the cost function?
ii.Derive the revenue function?
iii.Derive the profit function?
iv.Calculate the profit (loss) corresponding to production levels of 6,000 and 14,000 drinks respectively.

Thank you alot.

#### tkhunny

##### Moderator
Staff member
Hi, can anyone help me with this problem. I dont really understand how it is to be done.

A drink manufacturer has a monthly fixed cost of $24,000 and a production cost of$7 for each
drink produced.The product sells for $10 per drink. i. Derive the cost function? ii.Derive the revenue function? iii.Derive the profit function? iv.Calculate the profit (loss) corresponding to production levels of 6,000 and 14,000 drinks respectively. Thank you alot. Well, do it. It appears to be linear function for cost. Let's see your efforts. #### sura0912 ##### New member What is have so far is: cost function= 24000+7x revenue function= 10x profit function= 10x- (7x+24000) = 3x-24000 how do i find the answer to question iv? i would appreciate any help... thanks. #### JeffM ##### Elite Member Hi, can anyone help me with this problem. I dont really understand how it is to be done. A drink manufacturer has a monthly fixed cost of$24,000 and a production cost of $7 for each drink produced.The product sells for$10 per drink.

i. Derive the cost function?
ii.Derive the revenue function?
iii.Derive the profit function?
iv.Calculate the profit (loss) corresponding to production levels of 6,000 and 14,000 drinks respectively.

Thank you alot.
I am not sure what you do not know.

Do do you know the general formulas for the revenue, cost, and profit functions of a one-product firm in elementary microeconomics? All three general formulas should be mentioned prominently in your text or notes. The revenue function should talk about prices and the demand function. The cost function might talk about fixed costs and variable costs. Ring any bells?

Furthermore, the problem as you have reported it does not give sufficient information to create a revenue or profit function. Have you given us the complete problem?

#### stapel

##### Super Moderator
Staff member
What I have so far is as follows:

. . . . .cost function: C(x) = 24,000 + 7x

. . . . .revenue function: R(x) = 10x

. . . . .profit function: P(x) = 10x - (7x + 24,000)
. . . . . . . . . . . . . . . . . . ..= 3x - 24,000

How do I find the answer to question (iv)?
You have created a formula for the profit P(x) as a function of x. You have been given two values to plug into the formula, in place of x, and have been asked to find the corresponding values. So plug the given numbers into the derived formula, and simplify to obtain the requested information.

If you get stuck, or are not familiar with "evaluation" or "function", please reply showing how far you have gotten, and specifying where you are having trouble. Thank you!