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Question 1035341: I am lost with this.
A company that manufacturers snowboards has a fixed cost of $100,000. IT costs $175 to produce each snowboard.
The selling price of the snowboard is $300 each.
Use this information to answer:
a. Write the cost function
b. Write the revenue function
c. Find the profit function.
d. Determine the break even point. Describe what it means.
I have been trying for hours. Thank you
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I am lost with this.
A company that manufacturers snowboards has a fixed cost of $100,000. IT costs $175 to produce each snowboard.
The selling price of the snowboard is $300 each.
Use this information to answer:
a. Write the cost function:: C(x) = 100,000+ 175x where x is number of boards
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b. Write the revenue function:: R(x) = 300x where x is number of boards
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c. Find the profit function.
P(x) = R(x)-C(x) = 300x -(100,000+175x) = 125x - 100,000
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d. Determine the break even point. Describe what it means.
Breakeven means cost = revenue or profit = zero.
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Solve 125x - 100,000 = 0
125x = 100,000
x = 800 (# of boards made and sold)
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Cheers,
Stan H.
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Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! Problem:
A company that manufacturers snowboards has a fixed cost of $100,000. IT costs $175 to produce each snowboard.
The selling price of the snowboard is $300 each.
Use this information to answer:
a. Write the cost function
b. Write the revenue function
c. Find the profit function.
d. Determine the break even point. Describe what it means.
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Steps:
Part (a)
The fixed cost is $100,000. This means that even if the company fails to make a single board, they will pay $100,000 to buy the equipment, pay workers, pay rent, pay utilities, etc.
Let x = number of snowboards made
x snowboards are made, so it costs a total of 175*x dollars (because it costs $175 per board)
This is the variable cost.
Fixed cost = 100,000
Variable cost = 175*x
Total cost = (Variable Cost)+(Fixed Cost)
Total cost = (175*x)+(100000)
Total cost = 175*x+100000
So the cost function is
C(x) = 175*x+100000
where x represents how many boards were made and C(x) is the cost for making those x boards. Think of C(x) as one variable. It does NOT mean C times x. It's function notation.
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Part (b)
Let's still make x = number of snowboards made. Let's assume that the company manages to sell all x boards. So there are no boards leftover.
If x boards are sold, and they sell for $300 each, then the company gets 300*x dollars in revenue.
The revenue function is
R(x) = 300*x
x = number of boards made and sold
R(x) = revenue for selling x boards
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Part (c)
The profit is defined to be the difference of the revenue minus the costs.
Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = [ R(x) ] - [ C(x) ]
P(x) = [ 300*x ] - [ 175*x+100000 ]
P(x) = 300*x - 175*x-100000
P(x) = 125*x - 100000
Notice how this part (c) involves using parts (a) and (b)
So the profit function is
P(x) = 125*x - 100000
where
x = number of boards made and sold
P(x) = profit made total for selling x boards
The profit is the amount of money after all expenses are paid. In real life, there would be other expenses such as taxes, insurance, etc. But to make this problem simple, we're ignoring those factors.
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Part (d)
The break even point is when the profit is 0 dollars. You don't lose any money. And you don't gain any money.
Replace P(x) with 0. Then solve for x.
P(x) = 125*x - 100000
0 = 125*x - 100000
0+100000 = 125*x - 100000+100000 Add 100000 to both sides
100000 = 125*x
125*x = 100000
125*x/125 = 100000/125 Divide both sides by 125
x = 800
Here are 3 ways to say the same basic thing (they are equivalent statements)
- If you make and sell 800 boards, then you'll get a profit of $0.
- If you make and sell 800 boards, then you'll break even.
- If you make and sell 800 boards, then the cost (C(x)) is the same as the revenue (R(x))
If you make and sell more than 800 boards, then you'll get a positive profit. So this value is very useful for the manager in charge. Of course, keep in mind that other factors such as taxes, insurance, etc aren't considered in this particular problem. The same idea would apply though.
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Answers:
a) C(x) = 175*x+100000
b) R(x) = 300*x
c) P(x) = 125*x - 100000
d) Break even point happens when you sell 800 boards. It's where the profit is $0. No money is made or lost. The total cost is the same as the total revenue.
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