Question

write the constraints for the following situation. you are making cookies to sell at a school event. you are going to make chocolate chip cookies and sugar cookies. for the chocolate chip cookies, you will need 2 cups of flour and 3 cups of sugar. for the sugar cookies, you will need 3 cups of flour and 4 cups of sugar. you have a limited supply of flour and sugar and will not be buying anymore. in your pantry, you have 25 cups of flour and 30 cups of sugar. write the constraints if x represents the chocolate chip cookies and y represents sugar cookies.

\\(2x + 4x \leq 25\\)
\\(3y + 3y \leq 30\\)
\\(x \geq 0\\)
\\(y \geq 0\\)

\\(2x + 3y \geq 25\\)
\\(3x + 4y \geq 30\\)
\\(x \geq 0\\)
\\(y \geq 0\\)

\\(2x + 3y \leq 25\\)
\\(3x + 4y \leq 30\\)
\\(x \geq 0\\)
\\(y \geq 0\\)

\\(2x + 3x \leq 25\\)
\\(3y + 4y \leq 30\\)

Explanation:

Step1: Analyze Flour Constraint

Chocolate chip cookies (x) need 2 cups flour, sugar cookies (y) need 3 cups flour. Total flour used is \(2x + 3y\), and flour available is 25 cups. So \(2x + 3y \leq 25\).

Step2: Analyze Sugar Constraint

Chocolate chip cookies (x) need 3 cups sugar, sugar cookies (y) need 4 cups sugar. Total sugar used is \(3x + 4y\), and sugar available is 30 cups. So \(3x + 4y \leq 30\).

Step3: Non - negative Constraints

Number of cookies can't be negative, so \(x \geq 0\) and \(y \geq 0\).

Answer:

The correct option is the one with \(2x + 3y \leq 25\), \(3x + 4y \leq 30\), \(x \geq 0\), \(y \geq 0\) (the third option in the list of options provided).