1. A company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z. On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL. According to above information, what should be the company’s optimal product mix to maximize its profit? Construct the problem as a LP model. 2. Solve the above problem by using Simplex Method. 3. Min Z = 0.4 x1 + 0.5 x2 Subject to 0.3 x1 +0.1 x2 ≤ 2.7 0.5x1 +0.5x2 = 6 0.6 x1 + 0.4x2 ≥ 6 x1 - 2x2 ≥ 0 x1, x2 ≥ 0 Create a problem and define the decision variables to meet the following LP formulation. A LP model is constructed for you, you will just write down a problem according to this LP formulation.
1. A company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z.
On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL.
According to above information, what should be the company’s optimal product mix to maximize its profit? Construct the problem as a LP model.
2. Solve the above problem by using Simplex Method.
3. Min Z = 0.4 x1 + 0.5 x2
Subject to
0.3 x1 +0.1 x2 ≤ 2.7
0.5x1 +0.5x2 = 6
0.6 x1 + 0.4x2 ≥ 6
x1 - 2x2 ≥ 0
x1, x2 ≥ 0
Create a problem and define the decision variables to meet the following LP formulation. A LP model is constructed for you, you will just write down a problem according to this LP formulation.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images
