The problem involves a manufacturer of bicycle parts with fixed and variable costs, seeking to determine the cost when producing a specific number of units. The subject area includes cost functions, revenue functions, profit calculations, and break-even analysis.
There is ongoing exploration of the cost and revenue functions, with some participants providing guidance on how to structure the equations. Multiple interpretations of the problem are being discussed, particularly regarding the definitions of costs and revenues.
Participants express uncertainty about the formulas and the correct application of fixed and variable costs in the context of the problem. There are indications of confusion regarding the role of selling price in the cost function.
nae99 said:Homework Statement
A manufacturer of bicycle parts, has a monthly fixed cost of $25 000, a production cost of $21.75 per unit and a selling price of $325 per unit.
a) Cost function
b) Revenue function
c) Profit function
d) Break-even point
f) Cost when 150 units are produced.
Homework Equations
The Attempt at a Solution
a) 25 000 (x) =$21.75 (x) + $325
LCKurtz said:You need to put in more steps to lessen your confusion. Call the cost, revenue and profit functions for x units C(x), R(x), and P(x). To answer the first three parts, finish these three equations:
C(x) = ?
R(x) = ?
P(x) = ?
with formulas in terms of x on the right side. Then we can talk.
LCKurtz said:You need to put in more steps to lessen your confusion. Call the cost, revenue and profit functions for x units C(x), R(x), and P(x). To answer the first three parts, finish these three equations:
C(x) = ?
R(x) = ?
P(x) = ?
with formulas in terms of x on the right side. Then we can talk.
nae99 said:i am not sure about the formulas
C(x)= mx+b
R(x) = mx
P(x) = R(x) - C(x)
LCKurtz said:So what are m and b in this problem?
nae99 said:m= selling price
b= units
i think
LCKurtz said:But x is the number of units. I think you are just guessing. You just need to think about it some more. Here's a simpler example. If it costs me $100 to open my shop and $25 to build each widget, how much will it cost me total to build 3 widgets?
LCKurtz said:But x is the number of units. I think you are just guessing. You just need to think about it some more. Here's a simpler example. If it costs me $100 to open my shop and $25 to build each widget, how much will it cost me total to build 3 widgets?
nae99 said:it will cost $75
nae99 said:ok so it would be
C(x) = 325(x)+25 000
LCKurtz said:NO! What does the $325 have to do with the cost?
LCKurtz said:But x is the number of units. I think you are just guessing. You just need to think about it some more. Here's a simpler example. If it costs me $100 to open my shop and $25 to build each widget, how much will it cost me total to build 3 widgets?
LCKurtz said:What about the $100 rent (or salaries or whatever for that day)?
Once you answer that, what is the answer to build n widgets?
And if I sell n of them for $150 each, how much revenue will I get?
nae99 said:i don't know the formula, i think once i have the formula i will be able to do it
LCKurtz said:I am trying to help you understand how to figure out the formula. It would help if you would answer the widget questions I have posted above. Please don't edit some previous post; just reply to this one.
nae99 said:it will cost $175 to build n widgets
And if u sell n of them for $150 each, would get $450
LCKurtz said:Those are the answers for 3 widgets. What are the answers for n?
nae99 said:would n=3
LCKurtz said:You need to use n in the formulas instead of 3 if that's what you are asking. What do you get for both questions?
nae99 said:that's the thing, i don't know the formula
LCKurtz said:But you do know the formula if you just think about it. You answered both my questions for 3 widgets. You did a mental calculation to get those answers. You did a calculation using the number 3. Can you do the same calculation for 4 widgets? 5? 6?
Just describe the calculation you did but use n instead of a specific number. I know you can do it.
nae99 said:is it
n= 25(n) + 100
LCKurtz said:Almost. Since this is the Cost to make n widgets, why are you calling it n on the left side? Fix that and answer the second question; how much Revenue would I get from selling n widgets?
LCKurtz said:Almost. Since this is the Cost to make n widgets, why are you calling it n on the left side? Fix that and answer the second question; how much Revenue would I get from selling n widgets?
nae99 said:Revenue =150(n)
LCKurtz said:OK, finally you have cost and revenue:
C=100+25n and R = 150n so you can figure out profit =R - C.
Now notice that to get the total cost you took the fixed cost plus the number of items times the individual item cost. To get the revenue you took the selling price times the number of items. These formulas are no doubt in your text. To work your original problem you do the same thing. In that problem you are using x instead of n but the logic is the same and only the numbers are different.
LCKurtz said:OK, finally you have cost and revenue:
C=100+25n and R = 150n so you can figure out profit =R - C.
Now notice that to get the total cost you took the fixed cost plus the number of items times the individual item cost. To get the revenue you took the selling price times the number of items. These formulas are no doubt in your text. To work your original problem you do the same thing. In that problem you are using x instead of n but the logic is the same and only the numbers are different.
nae99 said:so for my original question it would be
C=25 000+325(21.75)
R=325(21.75)
LCKurtz said:Have you not understood anything I have said? What did n represent in my example? In my example everything is a function of n. There are no variables in your answer and it looks like you are just blindly plugging in all your numbers -- guessing again. Read the paragraphs I have quoted here and try to understand them.
Mark44 said:That's closer, but still not right. As you have it, it costs them $325 to make one bike, and they sell it for the same price.