Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.