What is the cost when 150 units are produced?

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Homework Help Overview

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.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formulation of cost, revenue, and profit functions, questioning the correct representation of fixed and variable costs. There are attempts to clarify the relationship between production costs and selling prices, as well as the need for proper definitions of variables in the equations.

Discussion Status

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.

Contextual Notes

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.

  • #31
Mark44 said:
Yes, that's better.

and Revenue will be
R = 21.75(x)
 
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  • #32
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.
 
  • #33
Mark44 said:
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
 
  • #34
nae99 said:
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)?
nae99 said:
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
 
  • #35
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
 
  • #36
These are all wrong.
nae99 said:
ok, so i should only put in the functions which are
c) Profit function P(x) = 325x - 25021.75x
How did you get this? P(x) = R(x) - C(x).
nae99 said:
d) Break-even point 325x= 21.75x + 25 000
The break-even point is the value of x for which C(x) = R(x).
nae99 said:
e) Cost of producing 150 bikes C = 150x + 25 000
The cost function is C(x) = 21.25x + 25,000. What is C(150)?
 
  • #37
ok, so the formulas are
profit = Revenue - cost P(x) = R(x) - C(x)

break even = C(x) = R(x)
are these right
and the Cost of producing 150 bikes will be C(150) = 21.25x + 25,000
 
  • #38
nae99 said:
ok, so the formulas are
profit = Revenue - cost P(x) = R(x) - C(x)
Yes, but what is P(x) in terms of the formulas for R(x) and C(x)?
nae99 said:
break even = C(x) = R(x)
are these right
Yes, and I wrote this already. Your job is to find the value of x for which C(x) = R(x).
nae99 said:
and the Cost of producing 150 bikes will be C(150) = 21.25x + 25,000
No, what you have on the right is C(x), not C(150). Evaluate your function at x = 150. Your answer should be a number - no x.
 
  • #39
You are just guessing. Plug in numbers until you get corrected enough times that the answer is correct. But you are showing absolutely no understanding of what you are doing. You will never learn how to analyze this kind of problem with that approach.

At this point, my best advice to you is to schedule an appointment with your teacher. I have done everything I can short of working the problem for you, which I will not do.
 
Last edited:
  • #40
d) Break-even point 325x= 21.75x + 25 000

The break-even point is the value of x for which C(x) = R(x)

R(x) = C(x)
325x = 21.75x + 25 000
325x - 21.75x = 25 000
13.25x = 25 000
13.25x/13.25 = 25 000/13.25
x = 1886.79
 
  • #41
nae99 said:
d) Break-even point 325x= 21.75x + 25 000

The break-even point is the value of x for which C(x) = R(x)

R(x) = C(x)
325x = 21.75x + 25 000
325x - 21.75x = 25 000
13.25x = 25 000
I can't even guess how you got 13.25x from the line above.
nae99 said:
13.25x/13.25 = 25 000/13.25
x = 1886.79
This is way off.
 
  • #42
Mark44 said:
I can't even guess how you got 13.25x from the line above.

This is way off.

oh sorry its suppose to be
325x = 21.75x + 25 000
325x - 21.75x = 25 000
303.25x = 25 000
303.25x/303.25 = 25 000/303.25
x= 82.440
 
  • #43
That looks like the right number. What does it represent?
 
  • #44
Mark44 said:
That looks like the right number. What does it represent?

it represent the break-even point
 
  • #45
Mark44 said:
That looks like the right number. What does it represent?

it represent the break-even point
 
  • #46
Have you done the last part yet? I.e., find the cost of making 150 bikes?
 
  • #47
Mark44 said:
Have you done the last part yet? I.e., find the cost of making 150 bikes?

No, because i am confuse
 
  • #48
Mark44 said:
a) Cost function. It is C(x) = 21.75x + 25,000

All you need to do is evaluate C(150) using the formula above.
 
  • #49
I don't think there is any need to continue this.
 

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