# 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 weekÃ¢Ã¢?Â¬Ã¢?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 Ã¢Ã¢?Â°Â¤ 48

Packaging hours: 2 X1 + 2 X2 Ã¢Ã¢?Â°Â¤ 18

Sales Potential: X1 < 6

Non-negativity: X1 Ã¢Ã¢?Â°Â¥ 0, X2 Ã¢Ã¢?Â°Â¥ 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.

https://brainmass.com/math/optimization/linear-programming-profit-optimization-444845

#### Solution Summary

LP is formulated and a graphical method is used to find the feasible region and optimized solution.