In Mathcad linear-programming problems are the problems in which it is required to optimize (define the maximum or minimum) the efficiency function, as given:

with the following imposed constraints:

One of the methods of solving such problems in Mathcad presupposes the use of the unit **given** with the functions of** minimize **and** maximize**. As an example, let’s consider the problem of planning the production of paints. The factory produces two kinds of paints **- I** and **Е**. Two constituent elements are in need for the manufacturing of paints - **А** and **В**. The maximum daily allowance of the constituent elements is: element **А** - **6 tons**; element **В** – **8 tons**. Consumption of the constituent elements for the manufacturing of 1 ton of paint is: paint **I - A/B= 2/1**; paint **Е**** - А****/В**** = 1/2**. Daily demand for paint **I** is never bigger than demand for paint **Е** more than **1 ton**. Demand for paint **I** is never bigger than **2 tons** a day. Wholesale prices are: paint **I – 2000 ****dollars** a ton, paint **Е**** – 3000 dollars** a ton. You are to define the maximum profit the factory can get after selling the paint. Let the daily flow of paint **I **be** x1**, and the daily flow of paint **Е **be **х****2**, then we get the economic-mathematical model of the problem, the model and the listing of its solution in Mathсad is shown in programme listing.

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