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Math Help - [SOLVED] objective quantities

  1. #1
    kari18
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    [SOLVED] objective quantities

    I need an objective quantity and all the constraints to determine the point of maximum profit..
    Chocolate covered peanuts are $40 for each case
    Chocolate covered pretzels are $55 for each case
    It takes a machine to 2 hours and a man 5 hours to make a case of peanuts
    and a machine 6 hours and a man 4 hours to make a case of pretzels
    there are only 150 machine hours and only 155 man hours available..
    I want to make the MAXIMUM profit!
    any help will be greatly appreciated
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  2. #2
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    Hello, kari18!

    I'll set it up for you . . .


    Determine the point of maximum profit.

    Chocolate covered peanuts are $40 for each case.
    Chocolate covered pretzels are $55 for each case.

    It takes a machine to 2 hours and a man 5 hours to make a case of peanuts
    and a machine 6 hours and a man 4 hours to make a case of pretzels.

    There are only 150 machine hours and only 155 man hours available.

    Let x = number of cases of peanuts: . x \:\geq \:0
    Let y = number of cases of pretzels: . y \:\geq\:0


    \begin{array}{cccccccc}<br />
&|& \text{Machine} &|& \text{Man} &|&\text{Profit} &| \\ \hline<br />
\text{Peanuts }(x) &|& 2x &|& 5x &|& 40x &| \\<br />
\text{Pretzels }(y) &|& 6y &|& 4y &|& 55y &| \\ \hline<br />
\text{Totals} &|& 150 &|& 155 &|\end{array}


    Constraints: . \begin{array}{ccc}2x + 6y & \leq & 150 \\<br />
5x + 4y & \leq & 155 \end{array} . and . \begin{array}{c}x \:\geq \:0 \\ y \:\geq \:0 \end{array}

    Profit function: . P \;=\;40x + 55y


    I assume you can finish it . . .

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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by Soroban View Post
    \begin{array}{cccccccc}<br />
&|& \text{Machine} &|& \text{Man} &|&\text{Profit} &| \\ \hline<br />
\text{Peanuts }(x) &|& 2x &|& 5x &|& 40x &| \\<br />
\text{Pretzels }(y) &|& 6y &|& 4y &|& 55y &| \\ \hline<br />
\text{Totals} &|& 150 &|& 155 &|\end{array}
    Let's improve your table:

     <br />
\begin{array}{*{20}c}<br />
{} &\vline & {{\text{Machine}}} &\vline & {{\text{Man}}} &\vline & {{\text{Profit}}} \\<br />
\hline<br />
{{\text{Peanuts}}\,(x)} &\vline & {2x} &\vline & {5x} &\vline & {40x} \\<br />
\hline<br />
{{\text{Pretzels}}\,(y)} &\vline & {6y} &\vline & {4y} &\vline & {55y} \\<br />
\hline<br />
{{\text{Totals}}} &\vline & {150} &\vline & {155} &\vline & {} \\<br />
\end{array}<br />

    (The LaTeX contribution of the day.)
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  4. #4
    Super Member

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    Hello, Krizalid!

    That's great . . . thanks!

    I knew about \hline, of course . . .
    . . but never suspected there was a \vline . . . *slap head*

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