Optimization Problems (I) Linear Programm Programming ing
Problem 1: A refinery has available two crude oils that have the yields shown in the following table. Because of equipment and storage limitations, production of gasoline, kerosene, and fuel oil must be limited as also shown in this table.
The profit on processing crude #1 is $1.00 /bbl and on crude #2 it is $0.70/bbl. Find the approximate optimum daily feed rates of the two crudes to this plant via a graphical method? Maximum allowable product rate (bbl/day)
Volume percent yields Crude #1
Crude # 2
70 6 24
31 9 60
Gasoline
Kerosene Fuel Oil
6000 2400 12000
Problem 2:
A company produces mixtures of canned fruits and has currently in the storage 10,000 kg of pears, 12,000 kg of lemons and 8,000 kg of cherries. Three different mixtures are produced and sold in 1 kg cans. First mixture has half pears and half lemons and is sold at a 30 pence profit. A second mixture has equal parts of the three fruits and sells at 40 pence profit. The third mixture contains half lemons and half cherries and yields a 50 pence profit per can. How many cans of each type should be produced for a maximum benefit? Problem 3:
There are three factories on the Moniss River (1, 2, and 3). Each emits two types of pollutants (1 and 2) into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $15 to process a ton of factory 1 waste, and each ton processed reduces the amount of pollutant 1 by 0.10 ton and amount of pollutant 2 by 0.45 ton. It costs $10 to process a ton of factory 2 waste, and each ton processed will reduce the amount of pollutant 1 by 0.20 ton and the amount of pollutant 2 by 0.25 ton. It costs $20 to process a ton of factory 3 waste, and each ton processed will reduce the amount of pollutant 1 by 0.40 ton and the amount of pollutant 2 by 0.30 ton. The state wants to reduce the amount of pollutant 1 in the river by at least 30 tons and the amount of pollutant 2 in the river by at least 40 tons. Formulate and LP that will minimize the cost of reducing pollution by the desired amounts. Find the optimum decision variables using using linprog in Matlab?
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Optimization Problems (I) Linear Programming
Problem 4: A chemical manufacturing firm has discontinued production of a certain unprofitable product line. This has created considerable excess production capacity on the three existing batch production facilities. Management is considering devoting this excess capacity to one or more of three new products: Call them products 1,2, and 3. The available capacity on the existing units that might limit output is summarized in the following table:
Unit A B C
Available time (h/week) 20 10 5
Each of the three new products requires the following processing time for completion:
Unit A B C
Product 1 0.8 0.4 0.2
Productivity (h/batch) Product 2 0.2 0.3
Product 3 0.3
0.1
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 batches per week. The profit per batch is $20, $6, and $8, respectively, on products 1, 2, and 3. Formulate a linear programming model for determining how much of each product the firm should produce to maximize profit.
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