Question

question 3 (4.5 points) 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 ≤ 25 3y + 3y ≤ 30 x ≥ 0 y ≥ 0 2x + 3y ≤ 25 3x + 4y ≤ 30 x ≥ 0 y ≥ 0 2x + 3y ≥ 25 3x + 4y ≥ 30 x ≥ 0 y ≥ 0 2x + 3x ≤ 25 3y + 4y ≤ 30 x ≥ 0 y ≥ 0

Explanation:

Step1: Determine flour - constraint

Each chocolate - chip cookie ($x$) needs 2 cups of flour and each sugar cookie ($y$) needs 3 cups of flour. The total amount of flour available is 25 cups. So the flour - constraint is $2x + 3y\leq25$.

Step2: Determine sugar - constraint

Each chocolate - chip cookie ($x$) needs 3 cups of sugar and each sugar cookie ($y$) needs 4 cups of sugar. The total amount of sugar available is 30 cups. So the sugar - constraint is $3x + 4y\leq30$.

Step3: Non - negativity constraints

The number of chocolate - chip cookies $x$ and sugar cookies $y$ cannot be negative. So $x\geq0$ and $y\geq0$.

Answer:

$2x + 3y\leq25$
$3x + 4y\leq30$
$x\geq0$
$y\geq0$
So the correct option is the second one:
$2x + 3y\leq25$
$3x + 4y\leq30$
$x\geq0$
$y\geq0$