A coffee powder provider works out the vairable cost of each kg is $2.50 with fixed cost of $30. He sells it to his distributors at $3 per kg. Find the cost function and revenue function if the amount of coffee is produced at x kg.

I'm stuck here! C(x)=30+2.5x
C(x)-2.5=30

C(x)=30+2.5x

This is good, the other one, however, is not. One more thing, it is always good to define what you are writing. What is x here? It's better to say somewhere, "Let x represent the number of kg of coffee.". Then, you say the cost of coffee, C(x) is given by...

This is the cost that the provider has to pay to get the coffee.

Now what is the function that gives the amount of money he gets by selling the coffee? Remember, he sells each kg of coffee at $3 per kg.

Post that, then we will move on to the last part.

Huh. But how to go about finding the function. I'm abit blur about the question. To find c or x

Just find the money he gets for the time being.

Let's say you buy an article for $40 and sell it for $50, what amount of money are you getting back?

Now, let's extent it a little, You buy 200 such items at $40 and sell them for $50 each. How much money are you getting by selling those?

Now, apply the same concept for your problem.

The last step is to find the profit, or loss. But I want you to get the money he receives first.

So he gets $0.50 per kg for selling the coffee?

This isn't what I would understand by that statement...

"He sells it to his distributors at $3 per kg"

Huh what you mean. But the problem is I don't know how much kg he sell. After calculating, he earn $0.50 per kg he sold.

That's why I told you to define your variables first.

"but the problem is i dont know how much kg he sell."

He sold all the coffee he had, that is, he sold x kg of coffee! :)

the variable cost is $2.50 X no of kg which is equal to 2.5x?

Can anyone show me the steps to do it?

Yes, that's the cost, or what you initially called 'Buying price' in small classes. Now I want you to get the 'Selling price'.

The selling price is 3 per kg?

Yes. Now, you already defined the number of kg as being x. What is the total selling price?

3x??

Yes, that's what I was asking you for.

Okay, the cost price is C(x) = 30 + 2.5x

The selling price is S(x) = 3x

Now the profit/loss is how much?

Remember that Profit/loss = Selling Price - Cost Price.

but the cost price is an equation. How to subtract?

Yes, they are both equations, treat them as any normal number, and let's see what happens. Wrap the equation in brackets just you minimise the risk of making mistakes. :)

3x - (Cx=30+2.5x)?

[Notice that revenue is also called selling price ;) ]

Okay, like this:

Selling price - Cost price = Profit/Loss

S(x) - C(x) = Profit/loss

So,

(3x) - (30 + 2.5x) = Profit/Loss

Profit/Loss = (3x) - (30 + 2.5x)

Can you find the function of the profit/loss?

So profit/loss = 5.5x - 30?