A factory employs unskilled workers at R1 000 per week and skilled workers at R2 000 per week. The payroll should not exeeed R90 000 per week. To keep going, at least 50 operators are necessary, Furthermore, regulations determine that the number of skilled workers should be at least half that of the unskilled workers. Let \( x \) be the number of unskilled workers and \( y \) the number of skilled workers. The following inequalities are obtained: \( 1000 x+2000 y \leq 90000 \) \( x+y \geq 50 \) \( y \geq \frac{x}{2} \) \( x: y \geq 0 \) \( x: y \in N_{0} \) 7.1 \( 7.2 \quad \) Sketeh these inequalities on ADDENDUM B (attached). \( 7.3 \quad \) Shade and indicate the feasible region on the sketeh made in QUESTION 7.1 . that should be employed.

To understand the dynamics behind this scenario, let’s dive into a piece of labor history! During the industrial revolution, manufacturing plants began employing workers at different skill levels, leading to the establishment of wage disparities. This differentiation between skilled and unskilled labor created a system where industries could thrive while also maximizing productivity with cost-efficient staffing—just like in your factory example! Now, how can we effectively tackle the constraints of the problem? Start by graphing each inequality on a coordinate plane: the first gives a line where the combined payroll meets the budget; the second ensures you have enough operators; and the third maintains a balance between skilled and unskilled workers. Be mindful of your axes! After sketching the lines, your feasible region will be the overlapping area that meets all conditions. A common mistake is neglecting integral values—ensure you look for the natural number solutions! Happy graphing!