MYP Extended Mathematics Systems of Inequalities Questionbank

A feasible region is defined by the following constraints: $x \ge 0$, $y \ge 0$, $x + 2y \le 8$, and $x + y \le 6$. Find the coordinates of the vertex that is the intersection of the two non-axis boundary lines.

Solve the inequality for $x$:

A bakery makes $x$ loaves of bread and $y$ cakes. Each loaf needs 3 cups of flour and each cake needs 2 cups. The bakery has a maximum of 60 cups of flour available. Which inequality represents this constraint?

![ A coordinate plane showing a dashed line that intersects the y-axis at 3 and the x-axis at 4. The region below and to the left of the line, including the origin (0,0), is shaded. ] Identify the inequality representing the shaded region.

In a linear programming maximization problem with the objective function $Z = 12x + 15y$ and constraints $x \geq 0, y \geq 0, x + y \leq 10$, what is the value of the objective function at the vertex representing no production ()?