Given:

Let xi be the number of hours process which takes for “i” run per week where i=1,2,3. Let Oi be the number of barrels of oil and G2 be the barrels of gas 2 sold per week.

Objective function:

The processor 1 that runs for 1 hour requires 2 barrels of crude oil 1 and 3 barrels of crude oil 2 and the output of process 1 for one hour produces 2 barrels of gas 1 and 1 barrel of gas 2.

The processor 2 that runs for 1 hour requires 2 barrels of crude oil 1 and 3 barrels of crude oil 2 and the output of process 2 for one hour produces 3 barrels of gas 2.

The process 3 that runs for 1 hour requires 2 barrels of crude 2 and 2 barrels of gas 2 and the output of process 3 for one hour produces 2 barrels of gas 3.

The revenue from the gas 1 is sold for $9 and the revenue from gas 3 is sold for $24 is 24(2x3). Here, the variable for gas 2 is sold and the remaining gas will be used in producing gas 3.

Maximize z=9(2x1)+10G2+24(2x3)−5x1−4x2−x3−2O1−3O2 =13x1−4x2+47x3+10G2−2O1−3O2

Considering the constraints,

Constraint 1: Total oil 1 used in process 1 and 2.

Constraint 2: Total oil 2 used in process 1,2 and 3.

Constraint 3 and 4: Each week, 200 barrels of crude oil 1 and 300 barrels of crude oil 2 must be purchased.

Constraint 4: Production gas 2 will be equal to the gas 2 sold and gas 2 used in 3 that have been produced by process 1 and 2 by using the amount of gas 2 produced and from each process.

Constraint 6: Each week, 100 hours of time catalytic crackers are available.

Expressing the constraint 1 in terms of x1, x2and x3 :

(2barrel of oil 1 used for process 1)+(1 barrel of oil 2 used for process 2)=O1 2x1+x2=O1 2x1+x2−O1=0

Expressing the constraint 2 in terms of x1,

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.8, Problem 14P

Chapter 3.9, Problem 2P

Students have asked these similar questions

A company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 800 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 trucks, 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, 1500 per day could be assembled, whereas if the assembly shop were completely devoted to assembling truck 2 engines, 1200 per day could be assembled. It is possible, however, to paint both types of trucks in the painting shop. Similarly, it is possible to assemble both types in the assembly shop. Each type 1 truck contributes $1000 to profit; each type 2 truck contributes $1500. Use Solver to maximize the company’s profit

A company owns the same asset in a ASIAN plant and in a UK plant . It has B $2,000,000 and a salvage value of 20% of B . For tax depreciation purposes, ASIA allows a straight line write-off over 5 years, while the UK allows SL write-off over 8 years. The general managers of the two plants want to know the difference in the depreciation amount for year 5.

The Mayfree Appliance Company requires sheet metal for its appliances. The company can purchase long coils of sheet metal in two different widths: 65 inches and 40 inches. The company must purchase the coils by linear foot of length: $1.20 per foot for a 64-inch coil and $1.00 per foot for a 40-inch coil. (This implies that a square foot, say, of the wider coil is less expensive.) Up to 4000 feet of the 65-inch coil is available, and up to 6000 feet of the 40-inch coil is available. There are manufacturing requirements for six different widths: 50, 45, 40, 35, 20, and 10 inches. Mayfree’s requirements are expressed as lengths of the various widths. The company requires 1000 feet of 50-inch width, 2500 feet of 45-inch width, 3000 feet of 40-inch width, 2300 feet of 35-inch width, 1300 feet of 20-inch width, and 2000 feet of 10-inch width. Determine how much of each width coil Mayfree should purchase and how it should cut the coils into various widths to meet its requirements at minimal…

Chapter 3 Solutions

Introduction to mathematical programming

Ch. 3.1 - Prob. 1P Ch. 3.1 - Prob. 2P Ch. 3.1 - Prob. 3P Ch. 3.1 - Prob. 4P Ch. 3.1 - Prob. 5P Ch. 3.2 - Prob. 1P Ch. 3.2 - Prob. 2P Ch. 3.2 - Prob. 3P Ch. 3.2 - Prob. 4P Ch. 3.2 - Prob. 5P

Ch. 3.2 - Prob. 6P Ch. 3.3 - Prob. 1P Ch. 3.3 - Prob. 2P Ch. 3.3 - Prob. 3P Ch. 3.3 - Prob. 4P Ch. 3.3 - Prob. 5P Ch. 3.3 - Prob. 6P Ch. 3.3 - Prob. 7P Ch. 3.3 - Prob. 8P Ch. 3.3 - Prob. 9P Ch. 3.3 - Prob. 10P Ch. 3.4 - Prob. 1P Ch. 3.4 - Prob. 2P Ch. 3.4 - Prob. 3P Ch. 3.4 - Prob. 4P Ch. 3.5 - Prob. 1P Ch. 3.5 - Prob. 2P Ch. 3.5 - Prob. 3P Ch. 3.5 - Prob. 4P Ch. 3.5 - Prob. 5P Ch. 3.5 - Prob. 6P Ch. 3.5 - Prob. 7P Ch. 3.6 - Prob. 1P Ch. 3.6 - Prob. 2P Ch. 3.6 - Prob. 3P Ch. 3.6 - Prob. 4P Ch. 3.6 - Prob. 5P Ch. 3.7 - Prob. 1P Ch. 3.8 - Prob. 1P Ch. 3.8 - Prob. 2P Ch. 3.8 - Prob. 3P Ch. 3.8 - Prob. 4P Ch. 3.8 - Prob. 5P Ch. 3.8 - Prob. 6P Ch. 3.8 - Prob. 7P Ch. 3.8 - Prob. 8P Ch. 3.8 - Prob. 9P Ch. 3.8 - Prob. 10P Ch. 3.8 - Prob. 11P Ch. 3.8 - Prob. 12P Ch. 3.8 - Prob. 13P Ch. 3.8 - Prob. 14P Ch. 3.9 - Prob. 1P Ch. 3.9 - Prob. 2P Ch. 3.9 - Prob. 3P Ch. 3.9 - Prob. 4P Ch. 3.9 - Prob. 5P Ch. 3.9 - Prob. 6P Ch. 3.9 - Prob. 7P Ch. 3.9 - Prob. 8P Ch. 3.9 - Prob. 9P Ch. 3.9 - Prob. 10P Ch. 3.9 - Prob. 11P Ch. 3.9 - Prob. 12P Ch. 3.9 - Prob. 13P Ch. 3.9 - Prob. 14P Ch. 3.10 - Prob. 1P Ch. 3.10 - Prob. 2P Ch. 3.10 - Prob. 3P Ch. 3.10 - Prob. 4P Ch. 3.10 - Prob. 5P Ch. 3.10 - Prob. 6P Ch. 3.10 - Prob. 7P Ch. 3.10 - Prob. 8P Ch. 3.10 - Prob. 9P Ch. 3.11 - Prob. 1P Ch. 3.11 - Show that Fincos objective function may also be...Ch. 3.11 - Prob. 3P Ch. 3.11 - Prob. 4P Ch. 3.11 - Prob. 7P Ch. 3.11 - Prob. 8P Ch. 3.11 - Prob. 9P Ch. 3.12 - Prob. 2P Ch. 3.12 - Prob. 3P Ch. 3.12 - Prob. 4P Ch. 3 - Prob. 1RP Ch. 3 - Prob. 2RP Ch. 3 - Prob. 3RP Ch. 3 - Prob. 4RP Ch. 3 - Prob. 5RP Ch. 3 - Prob. 6RP Ch. 3 - Prob. 7RP Ch. 3 - Prob. 8RP Ch. 3 - Prob. 9RP Ch. 3 - Prob. 10RP Ch. 3 - Prob. 11RP Ch. 3 - Prob. 12RP Ch. 3 - Prob. 13RP Ch. 3 - Prob. 14RP Ch. 3 - Prob. 15RP Ch. 3 - Prob. 16RP Ch. 3 - Prob. 17RP Ch. 3 - Prob. 18RP Ch. 3 - Prob. 19RP Ch. 3 - Prob. 20RP Ch. 3 - Prob. 21RP Ch. 3 - Prob. 22RP Ch. 3 - Prob. 23RP Ch. 3 - Prob. 24RP Ch. 3 - Prob. 25RP Ch. 3 - Prob. 26RP Ch. 3 - Prob. 27RP Ch. 3 - Prob. 28RP Ch. 3 - Prob. 29RP Ch. 3 - Prob. 30RP Ch. 3 - Prob. 31RP Ch. 3 - Prob. 32RP Ch. 3 - Prob. 33RP Ch. 3 - Prob. 34RP Ch. 3 - Prob. 35RP Ch. 3 - Prob. 36RP Ch. 3 - Prob. 37RP Ch. 3 - Prob. 38RP Ch. 3 - Prob. 39RP Ch. 3 - Prob. 40RP Ch. 3 - Prob. 41RP Ch. 3 - Prob. 42RP Ch. 3 - Prob. 43RP Ch. 3 - Prob. 44RP Ch. 3 - Prob. 45RP Ch. 3 - Prob. 46RP Ch. 3 - Prob. 47RP Ch. 3 - Prob. 48RP Ch. 3 - Prob. 49RP Ch. 3 - Prob. 50RP Ch. 3 - Prob. 51RP Ch. 3 - Prob. 52RP Ch. 3 - Prob. 53RP Ch. 3 - Prob. 54RP Ch. 3 - Prob. 56RP Ch. 3 - Prob. 57RP Ch. 3 - Prob. 58RP Ch. 3 - Prob. 59RP Ch. 3 - Prob. 60RP Ch. 3 - Prob. 61RP Ch. 3 - Prob. 62RP Ch. 3 - Prob. 63RP

Knowledge Booster