Methods of optimal solutions part 1 Witte Control

Option 1
Situation 1
Construct a mathematical model of the problem of production optimization. The enterprise produces four types of products P1-P4, for the production of which three types of resources are used: labor, raw materials and equipment. The consumption rates of each type of resource for the manufacture of a unit of each type of products are given in the table.

Resource Type of product Volume of resource
П1 П2 П3 П4
Labor 1 1 1 1 16
Raw materials 6 5 4 3 110
Equipment 4 6 10 13 100

The profit received from the sale of a unit of production is equal to: for production P1 - 60 cu, for P2 - 70 cu, for P3 - 120 cu. And for P4 - $ 130 Determine the optimal production plan for each product, maximizing the profit of the enterprise.


Situation 2
Construct a mathematical model of the problem. Create a problem that is dual to the original one. Based on the specialization and its technological capabilities, the enterprise can produce 4 types of products. Sales of any quantity are secured. For the production of these products, labor resources, semi-finished products and machine tools are used. The total amount of resources (per work week), the expenditure of each resource per unit of output and the price received per unit of output, are given in the table. It is required to determine the release plan that delivers the maximum revenue to the enterprise.

Resources Production
П1 П2 П3 П4
Р1 Labor resources, person hours 4 2 2 8 4800
P2 Semi-finished products, kg 2 10 6 0 2400
P3 Machine tools, machine tool 1 0 2 1 1500
Profit, USD 65 70 60 120

Situation 3.

Solve the transport problem using Excel computational tools. There are n production points and m distribution points. The cost of transportation of a unit of production from the i-th point of production to the j-th distribution center Cij is given in the table, where under the line is understood the point of production, and under the column - the distribution point. In addition, in this table, the i-th line indicates the volume of production at the i-th production point, and the j-th column indicates the demand in the j-th distribution center. It is necessary to draw up a transportation plan for the delivery of the required products to the distribution points, which minimizes the total transport costs.



Unit transportation cost Volume of production
1 3 4 5 20
5 2 10 3 30
3 2 1 4 50
6 4 2 6 20
Volumes of consumption 30 20 60 15

Situation 4.

Solve the problem of appointing teachers to conduct classes in accordance with a given table.

Teachers Cost of performance
1 2 3 4 5
1 310 300 600 520 700
2 500 200 720 800 350
3 320 550 100 590 200
4 600 240 200 980 450