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Thread: It cost $400 to manufacture a table. In addition, the overhead fixed cost associated

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    Question It cost $400 to manufacture a table. In addition, the overhead fixed cost associated

    It cost $400 to manufacture a table. In addition, the overhead fixed cost associated with production stands at $4000. The company manufactures 1 to a 100 tables daily. Records show the company demand is 10 tables the price is $1200, but when the demand is 30 tables the price is $200. Find the revenue, cost, price and profit function?

    This is what I have done so far. gradient is 1200-200/30-10 = 50 "gradient is 50".
    price p(x)=400-50x
    revenue R(x)=x(400-50x)=400x-50x^2

    I know how to get the profit function P(x)= R(x)-C(x) but I'm confused where the cost function is concern.

    Do I use the gradient in variable cost C(x)=1200+50x or 4000=1200+m(10) and find for m.......

    Please help guide me with the cost function and let me know if I'm correct with my price and revenue function, really want to understand how to interpret this question. Thank You in Advance.

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    Elite Member stapel's Avatar
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    Quote Originally Posted by Jason Superville View Post
    It cost $400 to manufacture a table. In addition, the overhead fixed cost associated with production stands at $4000. The company manufactures 1 to a 100 tables daily. Records show the company demand is 10 tables the price is $1200, but when the demand is 30 tables the price is $200. Find the revenue, cost, price and profit function?

    This is what I have done so far. gradient is 1200-200/30-10 = 50 "gradient is 50".
    I will guess that a linear relationship is being assumed (or was specified somewhere), that the "slope" formula was munged (here), that grouping symbols were omitted, and that you mean the following:

    . . .assuming linear relation between price and production:

    . . . . .[(1200 - 200) demanded] / [(10 - 30) unit price] = 1000 demanded / -20 unit price

    . . . . . .. .= -500 demanded per $1 increase in unit price

    But where did "50" come from?

    Quote Originally Posted by Jason Superville View Post
    price p(x)=400-50x
    What is your reasoning here? Why are you subtracting "50x" from the per-unit materials cost? Where do you account for the fixed overhead costs? For what does "x" stand?

    Please be complete. Thank you!

  3. #3
    Quote Originally Posted by stapel View Post
    I will guess that a linear relationship is being assumed (or was specified somewhere), that the "slope" formula was munged (here), that grouping symbols were omitted, and that you mean the following:

    . . .assuming linear relation between price and production:

    . . . . .[(1200 - 200) demanded] / [(10 - 30) unit price] = 1000 demanded / -20 unit price

    . . . . . .. .= -500 demanded per $1 increase in unit price

    But where did "50" come from?


    What is your reasoning here? Why are you subtracting "50x" from the per-unit materials cost? Where do you account for the fixed overhead costs? For what does "x" stand?

    Please be complete. Thank you!
    thank you I saw my error, it will be "-500" as the gradient. the subtracting supposed to be the price function formula p(x)=c-mx "c" is for constant or fixed cost, "x" stands for units or amount of tables sold.

    50x is the gradient which is wrong, but was I supposed to put the "per table cost as the variable" and "fixed overhead cost as fixed cost" e.g. "p(x)=4000-500x".

    Also should the gradient be used in the cost function as "C(x)=1200+(-500x) or do I still used one of the linear relations to find m C(x)=1200+m(10).

  4. #4
    Quote Originally Posted by stapel View Post
    I will guess that a linear relationship is being assumed (or was specified somewhere), that the "slope" formula was munged (here), that grouping symbols were omitted, and that you mean the following:

    . . .assuming linear relation between price and production:

    . . . . .[(1200 - 200) demanded] / [(10 - 30) unit price] = 1000 demanded / -20 unit price

    . . . . . .. .= -500 demanded per $1 increase in unit price
    I don't know what gradient is, but don't you mean: (1200 - 200) price / (10 - 30) unit = 1000 price / -20 units = -50 price per 1 unit increase in chairs.

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    Elite Member stapel's Avatar
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    Quote Originally Posted by ecoo View Post
    I don't know what gradient is...
    It's British-English for the American-English "slope".

    Quote Originally Posted by ecoo View Post
    ...but don't you mean: (1200 - 200) price / (10 - 30) unit = 1000 price / -20 units = -50 price per 1 unit increase in chairs.
    You're right, of course: 100/(-2) = -50, not -500. Oops!

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    Quote Originally Posted by Jason Superville View Post
    It cost $400 to manufacture a table. In addition, the overhead fixed cost associated with production stands at $4000. The company manufactures 1 to a 100 tables daily. Records show the company demand is 10 tables the price is $1200, but when the demand is 30 tables the price is $200. Find the revenue, cost, price and profit function?

    This is what I have done so far. gradient is 1200-200/30-10 = 50 "gradient is 50".
    price p(x)=400-50x
    revenue R(x)=x(400-50x)=400x-50x^2

    I know how to get the profit function P(x)= R(x)-C(x) but I'm confused where the cost function is concern.

    Do I use the gradient in variable cost C(x)=1200+50x or 4000=1200+m(10) and find for m.......

    Please help guide me with the cost function and let me know if I'm correct with my price and revenue function, really want to understand how to interpret this question. Thank You in Advance.
    To make sure I understand what you are doing lets's define a couple of things
    p = price of bike
    x = demand = number of bikes sold
    R = revenue = demand * price
    C = Cost = Fixed cost + per item cost
    P(x) = profit = R(x) - C(x)

    Given that, your price function is incorrect. You are correct in that the slope is -50 but the constant is incorrect, i:e. the form of the line is, in point slope form
    p(x) - 1200 = -50 (x - 10)
    That is when x is 10 then p is 1200 and when x is 30, the price is 200. This gives
    p(x) = 1700 - 50 x
    so
    R(x) = x p(x) = x (1700 - 50 x)
    Also,
    C(x) = 4000 + 400 x

    So, can you continue from there?

    -Ishuda

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