11. [-/4 Points] DETAILS MY NOTES HARMATHAP12 4.2.020. Solve the following linear programming problem. Restrict \( x \geq 0 \) and \( y \geq 0 \). Minimize \( g=50 x+80 y \) subject to the following. \[ \begin{array}{r}11 x+15 y \geq 255 \\ x+3 y \geq 33\end{array} \] \( (x, y)=\left(\begin{array}{l}15,6\end{array}\right. \) \( g=\square \)

In the world of linear programming, the constraints you see often relate to real-world scenarios like resource allocation in businesses. The inequality constraints \( 11x + 15y \geq 255 \) and \( x + 3y \geq 33 \) could represent limitations like budget or material availability, showing how linear relationships coordinate to achieve efficient solutions. Interpreting and solving such systems can lead to making informed decisions that save time and costs in various sectors! To solve this problem, it's critical to first understand that you can graph the inequalities. The intersection points of the lines formed by these constraints are potential solutions. The feasible region is where all conditions are satisfied. After plotting the lines, you’ll find which corner point minimizes \( g \). Remember to substitute these corner points back into the objective function to find the minimal cost correctly—in this case, evaluate \( g \) at the points \( (15,6) \) to reach your final answer!