# 4 задачи по ЭММ

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## Product description

Build on a plane region of admissible solutions of linear inequalities, and find the maximum and minimum values \u200b\u200bof the linear objective function in this area:
7x1 + 2x2 14
-x1 + x2 2
4x1 - x2 14 7
8 x1 + x2 9 72
x1 ≥ 0, x2 ≥ 0
F () = 14, x1 + x2 → extr 4
For the implementation of the three product groups of business it offers three types of limited material - financial resources in the amount of b1, b2, b3 units. At the same time for the sale of goods in the group 1 1 th. Rub. turnover of the first type of resource consumption in the amount of a11 units of the resource of the second type in the number of units a21, the resource of the third kind in the amount of a31 units. For sale 2 and 3 groups of products is 1 thousand rubles. turnover consumed respectively form a first resource amount a12, a13, units of the second kind of resources in an amount a22, a23 units, resources of the third kind in an amount of a32, a33 units. Profits from the sale of three product groups 1 thousand. Rub. turnover is respectively c1, c2, c3 (thousand. rub.).
Define the scope and structure of the planned turnover so that the profit of the company was trading at maximum
a11 = 3, a12 = 6, a13 = 4, a21 = 2, a22 = 1, a23 = 2, a31 = 2, a32 = 3, a33 = 1, b1 = 180, b2 = 50, b3 = 40, c1 = 6, c2 = 5, c3 = 5

Activity 3
Using the option number 2, you must specify:
- To direct the planning task turnover solved by the simplex method, make the dual problem of linear programming;
- Install a pair of conjugate variables primal and dual problems;
- According to the conjugate pairs of variables from the solution of the direct problem to obtain the solution of the dual problem, which assesses the resources spent for the sale of goods.

Suppliers of goods - wholesale businesses A1, A2, ........., Am are stocks of goods, respectively, in the amount of a1, a2, ......, am units. and retail trade enterprises B 1, B 2, ...., Bn - applied for the procurement of goods in amounts, respectively:
b1, b2, b3, ....., bn. Tariffs of cargo transport units on each of the points of delivery to the relevant items of consumption are given in the form of a matrix C (cij) (i =, j =) Find the plan of cargo transportation from suppliers to consumers, to the total cost of transportation were minimal.
a1 = b1 = 520 430
a2 = b2 = 480 115
a3 = b3 = 215 250
a4 = 85 b4 = 505
May 8th June 11
July 19 March 5
August 11 May 4

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