Problems:
Linear Programming for profit optimization
The Exeter Company produces two basic types of dog toys. Two resources are crucial to the output of the toys: assembling hours and packaging hours. Further, only a limited quantity of type 1 toy can be sold. The linear programming model given below was formulated to represent next weekââ?¬â?¢s situation.
Let, X1 = Amount of type A dog toy to be produced next week X2 = Amount of type B dog toy to be produced next week Maximize total contribution Z = 35 X1 + 40 X2 Subject to Extrusion hours: 4 X1 + 6 X2 ââ?°¤ 48 Packaging hours: 2 X1 + 2 X2 ââ?°¤ 18
Sales Potential: X1 < 6 Non-negativity: X1 ââ?°¥ 0, X2 ââ?°¥ 0
Use Excel Solver OR graphical method to find the optimal solution of the problem. If you use Excel Solver, please paste your output here.
Note 1: Place X1 along the horizontal axis and X2 along the vertical axi.
Note 2: Clearly mark the feasible region on the graph.
Note 3: Find the points of intersection points algebraically.
Note 4: Clearly show all steps to find the optimal solution by the graphical method.