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 х2, 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.