Thread: Can someone help with this Algebra 1 problem?

1. Can someone help with this Algebra 1 problem?

Baking a batch of chocolate chip cookies takes 1.75 cups of flour and 2 eggs.
Baking a batch of peanut butter cookies takes 1.25 cups of flour and 1 egg.

Paul has 10 cups of flour and 12 eggs.

He makes $4 profit per batch of chocolate chip cookies. He makes$2 profit per patch of peanut butter cookies.

How many batches of peanut butter cookies should Paul make to maximize his profits?

2. Originally Posted by Evelyn3131
Baking a batch of chocolate chip cookies takes 1.75 cups of flour and 2 eggs.
Baking a batch of peanut butter cookies takes 1.25 cups of flour and 1 egg.

Paul has 10 cups of flour and 12 eggs.

He makes $4 profit per batch of chocolate chip cookies. He makes$2 profit per patch of peanut butter cookies.

How many batches of peanut butter cookies should Paul make to maximize his profits?

Evelyn

It is very hard to help you with this problem because we have no idea what mathematical tools are in your personal tool kit.

Let's start by asking some questions. What is the highest number of batches of chocolate cookies (my favorites) that Paul can make, given that each batch requires 2 eggs and he has only 12 and each batch requires 1.75 cups of flour and he has only 10 cups? What would his profit be if he made that many batches of chocolate chips?

3. Hello, Evelyn3131!

Is there a typo?
This is not a "good" Linear Programming probem.

Baking a batch of CC cookies takes 1.75 cups of flour and 2 eggs.
Baking a batch of PB cookies take 1.25 cups of flour and 1 egg.
Paul has 10 cups of flour and 12 eggs.

He makes $4 profit per bath of CC cookies. He makes$2 profit per batch of PB cookies.

How many batches of PB cookies should Paul make to maximize his profit?

. . $\begin{array}{c|c|c|} & \text{flour} & \text{eggs} \\ \hline \text{CC (x)} & 1.75 & 2 \\ \text{PB (y)} & 1.25 & 1 \\ \hline \text{Total} & 10 & 12 \\ \hline \end{array}$

We have these inequalities: .$\begin{Bmatrix}1.75x + 1.25y \:\le\:10 \\ 2x + y \:\le\:12 \\ x\:\ge\:0 \\ y \:\ge\:0 \end{Bmatrix}$

Profit function: .$P \:=\:4x + 2y$

When we graph the two lines,
. . we find that they do not intersect in Quadrant 1.

The graph looks like this:

Code:
      |
|
*
| *
|   *
|     *
*       *
|  *      *
|     *     *
|        *    *
--+-----------*---*----
|

4. Code:
5 CC  :  8.75 cups + 10 eggs
1 PB  :  1.25 cups +  1 egg
============================
TOTAL : 10.00 cups + 11 eggs
5 @ $4 + 1 @$2 = \$22

And you have an egg left for breakfast

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