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 3 cups of flour and 3 cups of sugar. for the sugar cookies, you will need 1 cup 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 20 cups of flour and 30 cups of sugar. write the constraints if x represents the chocolate chip cookies and y represents sugar cookies.
○ $3x + 3x \leq 20$
$y + 4y \leq 30$
$x \geq 0$
$y \geq 0$
○ $3x + x \leq 20$
$3y + 4y \leq 30$
$x \geq 0$
$y \geq 0$
○ $3x + y \geq 20$
$3x + 4y \geq 30$
$x \geq 0$
$y \geq 0$
○ $3x + y \leq 20$
$3x + 4y \leq 30$

Explanation:

Step1: Analyze Flour Constraint

Chocolate chip cookies (x) need 3 cups of flour, sugar cookies (y) need 1 cup of flour. Total flour available is 20 cups. So the flour constraint is \( 3x + y \leq 20 \).

Step2: Analyze Sugar Constraint

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

Step3: Non - negativity Constraints

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

Answer:

The correct option is the last one: \( 3x + y \leq 20 \), \( 3x + 4y \leq 30 \), \( x \geq 0 \), \( y \geq 0 \)