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Math Help - another calculus question (functions)

  1. #1
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    another calculus question (functions)

    costs associated with manufacturing x products is described by:
    C(x)=x^3-7x^2+18x+110
    revenue for this level of manufacturing is : V(x)=3x^3-21x^2+84x+180

    Profit = V(x)-C(x)
    Calculate
    1. expression for profit associated with manufacturing x items
    2. how many items should be manufactured to minimise production costs
    3. how many items need to be manufactured to maximise the profit
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  2. #2
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    Hello, izaiyoi!

    This is very straight foward . . . Exactly where is your difficulty?


    Costs associated with manufacturing x products is described by:
    . . C(x)\:=\:x^3-7x^2+18x+110

    Revenue for this level of manufacturing is: . V(x)\:=\:3x^3-21x^2+84x+180

    \text{Profit }\:= \:P(x)\:=\:V(x)-C(x)


    Calculate:
    1. Expression for profit associated with manufacturing x items

    They told us that: . P(x) \:=\:V(x)-C(x) . . . didn't they?

    \text{So: }\;P(x) \;=\;\underbrace{\bigg[3x^3-21x^2+84x+180\bigg]}_{v(x)} - \underbrace{\bigg[x^3-7x^2+18x + 110\bigg]}_{C(X)} \;=\;\; ? ?



    2. How many items should be manufactured to minimise production costs?

    We want to minimize C(x).

    Solve: . C'(x) \:=\:0



    3. How many items need to be manufactured to maximise the profit?

    We want to maximize P(x).

    Solve: . P'(x) \:=\:0

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