Maximize Profit w/ Linear Programming: Omega Mfg Co

AI Thread Summary
Omega Manufacturing Company is exploring the use of its excess manufacturing capacity to produce three products, each with specific profit margins and machine hour requirements. The available machine hours are 550 for milling, 350 for lathe, and 150 for grinder. Product 1 has the highest profit potential at $50, followed by Product 3 at $25, and Product 2 at $20. Sales for Products 1 and 2 exceed their maximum production capabilities, while Product 3 has a sales limit of 20 units per week. The discussion seeks assistance in formulating a linear programming problem to maximize profits given these constraints.
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Homework Statement


Omega Manufacturing Company has excess manufacturing capacity and is considering
devoting its excess capacity to product 1,2, and 3.
The production process uses three types of machines and the available capacity on the machines is as follows:
Milling Machine: 550 hrs/week
Lathe 350 hrs/week
Grinder 150 hrs/week

Profits and machine requirements in hours for the three products are as follows:
Catagory Products 1 Product 2 Product 3
Profit 50 20 25
Milling Machine 9 3 5
Lathe 5 4 0
Grinder 3 0 2

Sales Potentials for Product 1 and 2 exceeds max production and Product 3 is expected to sell no more than 20 units per week. Formulate the LP PROBLEM

I really appreciate any help I can get on the problem. I have been struggling with it for sometime and I have a couple more like it so if I can see how to solve this one I can work through the rest. Thanks very much!
 
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Note: This is a 3 variable Linear Programming Problem
 
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