Hello! I came across the following question that appears easy. I was not able to construct the needed equation.

(1) The profit (in thousand of dollars) on x thousand units of a specialty item is given by p = 0.6x - 14.5. The cost c of manufactoring x thousand items is given by c = 0.8x + 14.5.

(A) Find an equation that gives the revenue r from selling x thousand items.

The correct equation is r = 1.4x but where did 1.4 come from? Is 1.4 the slope? If so, how is the slope produced using the given information above?

Someone suggested that profit = revenue - cost and that I should add the two given slopes 0.6 + 0.8 to get 1.4 as the new slope. However, profit = revenue MINUS cost not PLUS cost. Why do I need to add 0.6 and 0.8?

(B) How many items must be sold for the company to break-even?

I understood breaking-even to means when revenue equals cost.

I decided to let p = 0 in the profit equation given above and solve for x.

I got x = 24 but I am so far from the right answer. What did I do wrong?

2. Are you sure you have enough math for this course? This is not going to be easy if linear equation are foreign to you.

A simple model of production might be to break revenue into two components, 1) profit and 2) cost to produce. Thus Revenue = Profit + Cost. This model, with a little algebra, is exatly what "someone said".

We are given Profit and Cost. Simply adding them is sufficient.

(0.6x - 14.5) + (0.8x + 14.5)

After that, it is an algebra problem.

Note: If you are focused on the concept of slope and intercept, and cannot see just the algebra, you will continue to struggle. You do NOT have to know the meaning of each little symbol before you write it. Sometimes, you can just let the notation be the notation and move on. Get good at manipulating the notation. You are very unlikely to do this if you are hung up on the specific meaning of every jot and tittle.

3. ## Meaning of Profit

Originally Posted by TKHunny
Are you sure you have enough math for this course? This is not going to be easy if linear equation are foreign to you.

A simple model of production might be to break revenue into two components, 1) profit and 2) cost to produce. Thus Revenue = Profit + Cost. This model, with a little algebra, is exatly what "someone said".

We are given Profit and Cost. Simply adding them is sufficient.

(0.6x - 14.5) + (0.8x + 14.5)

After that, it is an algebra problem.

Note: If you are focused on the concept of slope and intercept, and cannot see just the algebra, you will continue to struggle. You do NOT have to know the meaning of each little symbol before you write it. Sometimes, you can just let the notation be the notation and move on. Get good at manipulating the notation. You are very unlikely to do this if you are hung up on the specific meaning of every jot and tittle.
I thought profit meant to subtract cost from revenue not add cost to revenue. If I knew the proper definition of profit, finding the slope would not have been a big deal.

4. Profit is the portion of revenue that exceeds the cost of production.

This is why I have chosen to challenge your algebra skills. You are arguing nothing. I explain:

You believe:

profit = revenue - cost

With the simplest possible algebra, adding 'cost' to both sides, we have

profit + cost = revenue

It simply does not matter which way you write it. You write it according to your needs.

One might also say:

cost = revenue - profit

Still the same thing. They are equivalent expressions. You should not be confused by this. You may wish to have a very serious chat with your acedemic advisor. Your math may need some upgrading. The mathematics you will need for this course will only get more difficult. If you are struggling already, you're toast.

I wish I had a better message for you. Maybe a good, committed tutor would help, but really, you MUST get your math up to speed immediately.

5. ## I got it.

Originally Posted by TKHunny
Profit is the portion of revenue that exceeds the cost of production.

This is why I have chosen to challenge your algebra skills. You are arguing nothing. I explain:

You believe:

profit = revenue - cost

With the simplest possible algebra, adding 'cost' to both sides, we have

profit + cost = revenue

It simply does not matter which way you write it. You write it according to your needs.

One might also say:

cost = revenue - profit

Still the same thing. They are equivalent expressions. You should not be confused by this. You may wish to have a very serious chat with your acedemic advisor. Your math may need some upgrading. The mathematics you will need for this course will only get more difficult. If you are struggling already, you're toast.

I wish I had a better message for you. Maybe a good, committed tutor would help, but really, you MUST get your math up to speed immediately.
I am not in a math course. I am reviewing certain areas of precalculus for the CST (Content Specialty Test).