Modeling is an art, and it takes practice. The following examples show dịch - Modeling is an art, and it takes practice. The following examples show Việt làm thế nào để nói

Modeling is an art, and it takes pr

Modeling is an art, and it takes practice. The following examples show the variety of problems that can be attacked by linear programming, and give you the opportunity to try your hand at some problems.
Exercise 44 A plant produces two types of refrigerators, A and B. There are two production lines, one dedicated to producing refrigerators of Type A, the other to producing refrigerators of Type B. The capacity of the production line for A is 60 units per day, the capacity of the production line for B is 50 units per day. A requires 20 minutes of labor whereas B requires 40 minutes of labor. Presently, there is a maximum of 40 hours of labor per day which can be assigned to either production line. Pro t contributions are $20 per refrigerator of Type A produced and $30 per Type B produced. What should the daily production be? Solve graphically and by Solver.

Exercise 45 Albert, Bill, Charles, David, and Edward have gotten into a bind. After a series of nancial transactions, they have ended up each owing some of the others huge amounts of money. In fact, near as the lawyers can make out, the debts are as follows

The question is, who is bankrupt? We will say that a person i is bankrupt if there is no possible transfer of funds among the people such that i completely pays o his obligations, and the transfer of funds satis es the following condition: for every two persons j and k, the amount paid by person j to person k is no greater than the debt of j to k. For instance, Albert is bankrupt since he owes 10, and is only owed 9. Formulate the problem of determining whether Bill is bankrupt as
a linear program. Then modify your formulation to determine if each of the others is bankrupt. This example may look contrived, but it is inspired by a solution to the debts involved in a crash of Kuwait's al-Mankh stock market.

Exercise 46 Due to an unexpected glut of orders, Blaster Steel has decided to hire temporary workers for a ve day period to clear out the orders. Each temporary worker can work either a two day shift or a three day shift for this period (shifts must be consecutive days). At least 10 workers are needed on days 1, 3, 5, and at least 15 workers are needed on days 2 and 4. A worker on a two day shift gets paid $125/day, while those on a three day shift gets paid $100/day.
(a) Formulate the problem of hiring temporary workers to minimize cost while meeting the
demand for workers.
(b) Due to a limited number of training personnel, no more than 10 workers can start their shift
on any day. Update your formulation in (a) to take this into account.
(c) Union regulations require that at least half of all money spent on workers go to those who work three day shifts. Update your formulation in (a) to handle this requirement.
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Modeling is an art, and it takes practice. The following examples show the variety of problems that can be attacked by linear programming, and give you the opportunity to try your hand at some problems.Exercise 44 A plant produces two types of refrigerators, A and B. There are two production lines, one dedicated to producing refrigerators of Type A, the other to producing refrigerators of Type B. The capacity of the production line for A is 60 units per day, the capacity of the production line for B is 50 units per day. A requires 20 minutes of labor whereas B requires 40 minutes of labor. Presently, there is a maximum of 40 hours of labor per day which can be assigned to either production line. Pro t contributions are $20 per refrigerator of Type A produced and $30 per Type B produced. What should the daily production be? Solve graphically and by Solver.Exercise 45 Albert, Bill, Charles, David, and Edward have gotten into a bind. After a series of nancial transactions, they have ended up each owing some of the others huge amounts of money. In fact, near as the lawyers can make out, the debts are as follows The question is, who is bankrupt? We will say that a person i is bankrupt if there is no possible transfer of funds among the people such that i completely pays o his obligations, and the transfer of funds satis es the following condition: for every two persons j and k, the amount paid by person j to person k is no greater than the debt of j to k. For instance, Albert is bankrupt since he owes 10, and is only owed 9. Formulate the problem of determining whether Bill is bankrupt asa linear program. Then modify your formulation to determine if each of the others is bankrupt. This example may look contrived, but it is inspired by a solution to the debts involved in a crash of Kuwait's al-Mankh stock market.Exercise 46 Due to an unexpected glut of orders, Blaster Steel has decided to hire temporary workers for a ve day period to clear out the orders. Each temporary worker can work either a two day shift or a three day shift for this period (shifts must be consecutive days). At least 10 workers are needed on days 1, 3, 5, and at least 15 workers are needed on days 2 and 4. A worker on a two day shift gets paid $125/day, while those on a three day shift gets paid $100/day.(a) Formulate the problem of hiring temporary workers to minimize cost while meeting thedemand for workers.(b) Due to a limited number of training personnel, no more than 10 workers can start their shifton any day. Update your formulation in (a) to take this into account.(c) Union regulations require that at least half of all money spent on workers go to those who work three day shifts. Update your formulation in (a) to handle this requirement.
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