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 week's situation.
Let, X_{1} = Amount of type A dog toy to be produced next week
X_{2} = Amount of type B dog toy to be produced next week
Maximize total contribution Z = 35 X_{1} + 40 X_{2}
Subject to
Assembling hours: 4 X_{1} + 6 X_{2} £ 48
Packaging hours: 2 X_{1} + 2 X_{2} £ 18
Sales Potential: X_{1} < 6
Non-negativity: X_{1} ³ 0, X_{2} ³ 0
Use Excel Solver to find the optimal solution of the problem. Please paste your output here.
Note 1: Place X_{1} along the horizontal axis and X_{2} 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.