Operations research control RIU t = 2
Replenishment date: 18.02.2015
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Description
t = 2
Task 1. The company produces animal feed and packs it in bags. Each bag contains two types of feed and is designed to feed one animal during the day. When fattening, each animal must receive at least 9 units of substance B1, at least 8 units. substance B2 and at least 12 units. substance B3. The content of the number of nutrient units in 1 kg of each type of feed and the cost of 1 kg of feed (in conventional monetary units) are shown in the table:
Nutrients Amount of nutrients in 1 kg of feed
Feed 1 Lump 2
B1 3 1
B2 1 2
B3 1 6
Feed cost 4 6
Formalize the production process, draw up a mathematical model. Describe the formalization process similarly.
To what class of operations research problems does this problem belong? Justify the answer.
What ways of finding optimal solutions can you suggest for this production?
Task 2. At two enterprises of the industry, it is necessary to make 200 products of some products. The costs associated with the production of x1 products at the first enterprise are equal to rubles, and the costs associated with the manufacture of products at the second enterprise are rubles. Determine how many products should be produced at each of the enterprises so that the total costs associated with the manufacture of the required products are minimal.
1. Formalize the production process, make a mathematical model. Describe the formalization process in detail.
2. To what class of operations research problems does this problem belong? Justify the answer.
3. What ways of finding optimal solutions can you suggest for this production.
Task 3. The manufacturing enterprise CJSC "Triumph", working in the same mode, can receive different profits depending on the composition of demand. Three such conditions were identified. In the best condition S1, the profit is 200 thousand rubles. profit on a monthly basis and could get even more if production capacity allowed. With an average state of demand S2, the Profit is 120 thousand rubles, and with a weak demand S3 - 50 thousand rubles. IN
Task 1. The company produces animal feed and packs it in bags. Each bag contains two types of feed and is designed to feed one animal during the day. When fattening, each animal must receive at least 9 units of substance B1, at least 8 units. substance B2 and at least 12 units. substance B3. The content of the number of nutrient units in 1 kg of each type of feed and the cost of 1 kg of feed (in conventional monetary units) are shown in the table:
Nutrients Amount of nutrients in 1 kg of feed
Feed 1 Lump 2
B1 3 1
B2 1 2
B3 1 6
Feed cost 4 6
Formalize the production process, draw up a mathematical model. Describe the formalization process similarly.
To what class of operations research problems does this problem belong? Justify the answer.
What ways of finding optimal solutions can you suggest for this production?
Task 2. At two enterprises of the industry, it is necessary to make 200 products of some products. The costs associated with the production of x1 products at the first enterprise are equal to rubles, and the costs associated with the manufacture of products at the second enterprise are rubles. Determine how many products should be produced at each of the enterprises so that the total costs associated with the manufacture of the required products are minimal.
1. Formalize the production process, make a mathematical model. Describe the formalization process in detail.
2. To what class of operations research problems does this problem belong? Justify the answer.
3. What ways of finding optimal solutions can you suggest for this production.
Task 3. The manufacturing enterprise CJSC "Triumph", working in the same mode, can receive different profits depending on the composition of demand. Three such conditions were identified. In the best condition S1, the profit is 200 thousand rubles. profit on a monthly basis and could get even more if production capacity allowed. With an average state of demand S2, the Profit is 120 thousand rubles, and with a weak demand S3 - 50 thousand rubles. IN
Additional Information
Under these conditions, the Board of Shareholders is considering expanding production by building a new workshop. There are two projects for such a workshop. Project A assumes that in the S1 state, the enterprise's profit will be increased by 100 thousand rubles, with the demand for S2, the profit will increase by 50 thousand rubles, and with the demand for S3, the enterprise will suffer losses in the amount of 50 thousand rubles. Project B assumes that in the state S1 the profit of the enterprise will be increased by 50 thousand rubles, with the demand for S2, the profit will increase by 10 thousand rubles, and with the demand S3 the profit of the enterprise will be only 10 thousand rubles.1. Determine the possible strategies of the enterprise and create a matrix of utility.
2. Determine the optimal strategy of the enterprise according to the Laplace criterion, conditionally accepting all states of demand as equally probable.
3. Determine the optimal strategy of the enterprise according to the Laplace criterion, if it is known that in t cases out of 10 the demand takes the best value, and the remaining two states are equally probable.
Task 4. According to the condition of task 3 (1), make a risk matrix.
1. Determine the risk-optimal strategy of the enterprise using the Laplace criterion, conventionally accepting all conditions of demand as equiprobable.
2. Determine the risk-optimal strategy of the enterprise using the Laplace criterion if it is known that in t cases out of 10 the demand takes the best value, and the remaining two states are equally probable.
Task 5. Captain Ivanov commands three detachments. There are two heights in front of him. He must decide how many detachments to send to capture each height. His opponent, Major Kovalev, also has three detachments under his command and must make the same decision. All units are assumed to be equal. If at one of the heights one of the opponents has a numerical superiority, then he captures this height. If not, then its height remains neutral territory. The player's payoff is equal to the number of heights captured.
1. How many pure strategies does each player have?
2. Formalize the situation by creating a game matrix. Make a conclusion.
3. Classify the game according to the 5 characteristics indicated in the tutorial.
Task 6. In front of each of the two players there are 4 cards with the numbers 1, 2, 3, t turned upside down. At the same time, both players turn over one card, choosing it at random. If the numbers match, there is no win. If there is a mismatch, the one with the lower number pays the second the difference between the dropped numbers.
1. Describe the formalization of this game situation, build the game matrix.
2. Classify the game according to the 5 characteristics indicated in the tutorial.
3. Find the solution to this game and interpret it based on the conditions of the problem.
Task 7. The administration of the shopping and entertainment center is considering the possibility of its reconstruction in order to annex additional territory to the center by demolishing old tents near the building. The reconstruction plan includes the demolition of old tents and the construction of new pavilions. The work that needs to be done and the execution time are indicated in the table.
Job Content Immediately preceding jobs Execution time (in weeks)
A Prepare a project - 5
B Identify future tenants - 6
C Prepare a project for tenants A 4
D Select contractor A 3
E Prepare documents for obtaining a building permit A 1
F Obtain a building permit E 4
G Build D, F 14
H Conclude contracts with tenants B, C 12
I Bring tenants to pavilions G, H t
1. Formalize the situation by building its network model.
2. Determine the critical path and its length and critical work by any known