Draw the feasible region of the Linear Programming Problem on a graph.

in Operations management

Question:

ABC Manufacturing Company is planning to optimize its production process for three of its products: P$1,$ P $2,$ and P $.$ The company has three machines: M$1,$ M$2,$ and M$3,$ which are required to complete the production of each product. The processing times $($in hours$)$ for each product on each machine are given in the table below. Additionally, the available hours for each machine per week are also provided.

$\backslash$table$[[\backslash$table$[[$Produc$],[$t$]],\backslash$table$[[$Machin$],[$e $1],[($M$1)]],\backslash$table$[[$Machin$],[$e $2],[($M$2)]],\backslash$table$[[$Machin$],[$e $3],[($M$3)]]],[$P$1,4,3,2],[$P$2,2,2,3],[$P$3,3,4,2]]$

$\backslash$table$[[$Machine$,\backslash$table$[[$Available Hours$],[($per week$)]]],[$M$1,60],[$M$2,50],[$M$3,40]]$

Tasks:

Formulate a Linear Programming Problem $($LPP$)$ to determine the optimal production quantities of P $1,$ P $2,$ and P $3$ that maximize the total production given the machine constraints.

Draw the feasible region of the Linear Programming Problem on a graph.

Identify the corner points of the feasible region and calculate the total production at each corner point to find the optimal solution.

Instructions:

Formulate the objective function and the constraints for the LPP based on the given data.

Use graph paper or a graphing tool to plot the feasible region.

Clearly label the axes, constraints, and corner points on the graph.

Calculate the total production at each corner point to determine the optimal production quantities for P$1,$ P$2,$ and P$3.$

Note: Ensure to consider non$-$negativity constraints for the production quantities of P$1,$ P$2,$ and P$3.$