What is the cost when 150 units are produced?

[nae99]

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]

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

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.

 

[SteamKing]

Your equation a) contains a couple of mistakes. The monthly fixed costs are constant: no matter how many bicycles are made, it takes $25000 to keep the plant open and ready for production. The $325 selling price for each bike is not charged to the company unless it decides to buy a bike at retail.

You should also try to answer the other parts of the problem.

 

[nae99]

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.

i am not sure about the formulas
C(x)= mx+b
R(x) = mx
P(x) = R(x) - C(x)

 

[LCKurtz]

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.

i am not sure about the formulas
C(x)= mx+b
R(x) = mx
P(x) = R(x) - C(x)

So what are m and b in this problem?

 

[nae99]

So what are m and b in this problem?

m= selling price
b= units

C(x)= 325x+21.75

 

[LCKurtz]

m= selling price
b= units

i think

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]

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?

it will cost $75

 

[nae99]

ok so it would be
C(x) = 325(x)+25 000

 

[LCKurtz]

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?

it will cost $75

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?

 

[LCKurtz]

ok so it would be
C(x) = 325(x)+25 000

NO! What does the $325 have to do with the cost?

 

[nae99]

NO! What does the $325 have to do with the cost?

$325 is the selling price
i don't know the formula, i think once i have the formula i will be able to do it

 

[LCKurtz]

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?

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?

i don't know the formula, i think once i have the formula i will be able to do it

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]

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.

it will cost $175 to build n widgets

And if u sell n of them for $150 each, would get $450

 

[LCKurtz]

it will cost $175 to build n widgets

And if u sell n of them for $150 each, would get $450

Those are the answers for 3 widgets. What are the answers for n?

 

[nae99]

Those are the answers for 3 widgets. What are the answers for n?

would n=3

 

[LCKurtz]

would n=3

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]

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?

that's the thing, i don't know the formula

 

[LCKurtz]

that's the thing, i don't know the formula

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]

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.

is it
n= 25(n) + 100

 

[LCKurtz]

is it
n= 25(n) + 100

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]

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?

Revenue =150(n)

 

[LCKurtz]

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?

Revenue =150(n)

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]

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.

so for my original question it would be

C=25 000+325(21.75)
R=325(21.75)

 

[LCKurtz]

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.

so for my original question it would be

C=25 000+325(21.75)
R=325(21.75)

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]

No. Look at what LCKurtz has in post #23. Your Cost and Revenue functions should be in terms of the number of units that are manufactured.

In other words, C and R should involve x.

 

[nae99]

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.

C=25 000 + 325(x)

R= 325(x)

is that any good

 

[Mark44]

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.

 

[nae99]

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.

i am confused
C=25 000 + 21.75(x)
is that correct

 

[Mark44]

Yes, that's better.

 

[nae99]

Yes, that's better.

and Revenue will be
R = 21.75(x)

 

[Mark44]

No, you had it correct before in post #27. The company can't make any profit if they sell the bikes for the same as it costs to make them.

 

[nae99]

No, you had it correct before in post #27. The company can't make any profit if they sell the bikes for the same as it costs to make them.

ok so working out the cost function would it be

C(x) = 21.75(x) + 25 000
C(325) = 21.75(325) + 25 000
C(325) = 7068.75 + 25 000
C(325) = 32 068.75

 

[Mark44]

ok so working out the cost function would it be

C(x) = 21.75(x) + 25 000

Stop here.

Why are you calculating C(325)?

C(325) = 21.75(325) + 25 000
C(325) = 7068.75 + 25 000
C(325) = 32 068.75

Your problem is to find these:
a) Cost function. It is C(x) = 21.75x + 25,000
b) Revenue function. You have it - it is R(x) = 325x
c) Profit function
d) Break-even point
e) Cost of producing 150 bikes

 

[nae99]

ok, so i should only put in the functions which are
c) Profit function P(x) = 325x - 25021.75x
d) Break-even point 325x= 21.75x + 25 000
e) Cost of producing 150 bikes C = 150x + 25 000