Develop the complete model, clearly showing the decision variables, objective fu

Question

Develop the complete model, clearly showing the decision variables, objective function, and all constraints very clearly (assume the reader doesn't know much). Problem 2: The Omega Manufacturing Company has discontinued the production of a certain unprofitable product line. This created considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products: call them products 1, 2 and 3. The available capacity on the machines that would limit output is summarized in the following table: Machine TypeAvailable Time (Machine Hours per Week) Milling machine Lathe Grinder 500 350 150 The number of machine hours required for each unit of the respective products is shown in the following table: Product 1 Product 2 Milling machine Lathe Grinder 2 The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate, and that the sales potential for product 3 is 20 units per week. The unit profit would be $50, $20, and $25, respectively, on products 1, 2, and 3. The objective is to determine how much of each product Omega should produce to maximize profit. Develop a linear programming model that will be used to solve the problem.

Explanation / Answer

let x=number of units of product1

y=number of units of product 2

z= number of units of product3

given to maximize the profit

Maximize P=50x+20y+25z

subjected to

9x+3y+5z<=500 (milling machinee constraints)

5x+4y<=350(lathe constraints)

3x+2z<=150 (grinder constraints)

z<=20 (sale potential of product 3)

x,y,z>=0

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