1. ## [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

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

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

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

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

I assume you can finish it . . .

3. Originally Posted by Soroban
$\displaystyle \begin{array}{cccccccc} &|& \text{Machine} &|& \text{Man} &|&\text{Profit} &| \\ \hline \text{Peanuts }(x) &|& 2x &|& 5x &|& 40x &| \\ \text{Pretzels }(y) &|& 6y &|& 4y &|& 55y &| \\ \hline \text{Totals} &|& 150 &|& 155 &|\end{array}$

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

(The LaTeX contribution of the day.)

4. 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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