Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, he uses [tex]\( \frac{1}{3} \)[/tex] cup of oil and 2 eggs. For a tray of bran muffins, he uses [tex]\( \frac{1}{2} \)[/tex] cup of oil and 1 egg. Alan has 12 eggs on hand. He sells trays of blueberry muffins for [tex]$12 each and trays of bran muffins for $[/tex]10 each. To maximize the money raised at the bake sale, let [tex]\( x \)[/tex] represent the number of trays of blueberry muffins and [tex]\( y \)[/tex] the number of trays of bran muffins Alan bakes.

What are the constraints for the problem?

[tex]\[
\begin{array}{l}
\frac{1}{3} x + \frac{1}{2} y \leq 4 \\
2x + y \leq 12 \\
x \geq 0 \\
y \geq 0 \\
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Sure, let's outline the constraints given Alan's situation:

1. Alan uses [tex]\(\frac{1}{3}\)[/tex] cup of oil for each tray of blueberry muffins and [tex]\(\frac{1}{2}\)[/tex] cup of oil for each tray of bran muffins. Given that he has 4 cups of oil available, he needs to satisfy the constraint for oil usage:

[tex]\[ \frac{1}{3}x + \frac{1}{2}y \leq 4 \][/tex]

2. For eggs, Alan uses 2 eggs for each tray of blueberry muffins and 1 egg for each tray of bran muffins. Given that he has 12 eggs on hand, this results in the constraint for egg usage:

[tex]\[ 2x + y \leq 12 \][/tex]

3. Alan cannot bake a negative number of trays for either type of muffin, so the constraints for the number of trays baked are:

[tex]\[ x \geq 0 \][/tex]
[tex]\[ y \geq 0 \][/tex]

Combining these constraints, we have the following system of inequalities summarizing the problem:

[tex]\[ \begin{array}{l} \frac{1}{3}x + \frac{1}{2}y \leq 4 \\ 2x + y \leq 12 \\ x \geq 0 \\ y \geq 0 \\ \end{array} \][/tex]

Thus, these constraints must be satisfied in order to maximize the money raised at the bake sale.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.