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Problem 4: Module 8 (30 points)

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, 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

Assembling hours: 4 X1 + 6 X2 48

Packaging hours: 2 X1 + 2 X2 18

Sales Potential: X1 < 6

Non-negativity: X1 0, X2 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.