Reference no: EM133045316
Assignment - "Mathematical modeling"
Case 1. West Siberian Corporation "Chemicals and Fertilizers".
In December. VasilyMaslov, general director of the West Siberian branch of the Corporation "Chemicals and Fertilizers", received a letter from Yuri Chernousov from the company "Sibirgaz". In the letter, the corporation was notified of the new procedure for the supply of natural gas. Sibirgaz, a supplier of natural gas to the corporation, reported a 40% reduction in gas supplies during the winter months. Approval from the Federal Energy Commission has already been obtained.2002 ?
When reducing, the following priorities apply (starting with the most undesirable option and ending with the more acceptable one):
1. Heating of housing and workplaces.
2. Commercial organizations using natural gas as a raw material.
3. Commercial organizations using natural gas as an industrial fuel.
Almost all of the corporation's production fell under priorities 2 and 3, therefore, the reduction in supplies was inevitable.
Job
1. Build a model and find production volumes while reducing gas supplies by (25 n)and (40-n)%.
2. Explain which product requires the most attention in terms of energy savings.
3. Answer the following questions:
What problems can be foreseen if production is not reduced as planned? What impact will the reduction in gas supplies have on the company's profits?
Case 2. The Sochi winery produces three brands of dry wine: "Black Prince", "Bouquet of Flowers" and "Acacia Flowers". Wholesale prices at which finished products are sold, respectively (60 +n),(45 + 2n) and(70-n)rubles. per liter. Ingredients for the preparation of these wines are white, pink and red dry wines purchased in Krasnodar. These wines cost respectively 70, 50 and 40 rubles. per liter. On average, the Sochi winery is supplied daily (1900+20n)l white, (2300+50n) l rose and(1000+30n)l red wine.
The wine "Black Prince" should contain at least 60% white wine and no more than 20% red. Wine "Bouquet of flowers" should contain no more than 60% red and at least 15% white. The total content of red and pink wine in the wine "Acacia Flowers" should not exceed 90%.
Identify recipes for mixing ingredients for the production of wines "Black Prince" and "Bouquet of Flowers", providing the plant with maximum profit.
Questions:
1. What is the maximum profit you can get in one day?
2. How many litres of Black Prince wine should I produce daily?
3. How many percent of white wine should the Black Prince contain?
4. How many liters of wine "Bouquet of Flowers" should be produced daily?
5. How many liters of wine "Acacia Flowers" should be produced daily?
6. How many percent of rose wine should contain "Acacia Flowers"?
7. How much will the profit of the winery increase if the supply of red wine can be increased by 300 liters per day?
8. How many rubles will the profit of the winery decrease if the supply of white wine is reduced by 200 liters per day?
Case 3. Vremya Ahead wants to develop a plan for assembling computers
Questions:
1. How many computers should be assembled in the first quarter to meet demand with minimal total costs?
2. How many percent should the capacity of the second shift be used in the first quarter?
3. How many computers should I build in the second quarter?
4. How many computers should be assembled in the second quarter in the second shift for sales in the third quarter?
5. What are the minimum costs?
6. How can costs change if the company manages to reduce the cost of storing each computer per quarter by 10%?
Case 4.The management of a certain company is negotiating with the trade union of workers and employees to conclude a contract.The matrix describes the profit of the union (player A) and the costs of the administration of the firm (player B).Find a solution to the game using the method of solving the problem to the solution of linear programming problems.
Case 5. Using balance ratios, complete the balance sheet.
Knowing the predicted values of the vector of gross product, calculate the vector of final consumption.
Case 6. Nthe same production can be described using the Cobb-Douglas function. Currently, one worker produces products per month for (40,000 + 800n) rubles. The total number of employees (350 + 3n)people. Fixed assets are estimated at (50 + 2n) millionrubles. It is known that to increase output by 5%, it is necessary to increase either the cost of funds by 10%, or the number of employees by (12 +n)%.
Required:
1) to make a Cobb-Douglas function for this production, determining the elasticity coefficients;
2) determine the average and marginal labor productivity;
3) determine the average and maximum capital output;
4) find norms of resource substitution and limit norms of resource substitution (give an economic interpretation of the obtained indicators);
5) determine the number of employees, if the value of fixed assets is increased by 3 times, reduced by 3 times.
Case 7. The gas station, which sells the most popular grade of gasoline, has two gas columns combined with terminals for accepting payment
Evaluate the main indicators of the effectiveness of the functioning of the gas station, evaluate them and carry out in two stages the adjustment of the model in order to increase economic efficiency. At the first stage, double the place for waiting for cars, at the second stage, increase the number of refueling columns by one unit.
Analyze the change in profit and profitability from the initial version of the functioning of the CMO to the final one. Assess the feasibility of reorganization. Formulate governing recommendations.
Attachment:- Mathematical modeling.rar