*Let x be the number of tables of type T1 and y the number of tables of type T2.Profit P(x , y) = 90 x 110 y \[ \begin \ x \ge 0 \ \ x \ge 0 \ \ 2x 4y \le 7000 \ \ x 2.5y \le 4000 \ \ 2x 1.5y \le 5500 \ \end \] .*

In the business world, people would like to maximize profits and minimize loss; in production, people are interested in maximizing productivity and minimizing cost.

However, there are constraints like the budget, number of workers, production capacity, space, etc.

The profit per unit of T1 is $90 and per unit of T2 is $110.

How many of each type of tables should be produced in order to maximize the total monthly profit?

Methods of solving inequalities with two variables, system of linear inequalities with two variables along with linear programming and optimization are used to solve word and application problems where functions such as return, profit, costs, etc., are to be optimized. The store owner pays $8 and $14 for each one unit of toy A and B respectively.

One unit of toys A yields a profit of while a unit of toys B yields a profit of .The following videos gives examples of linear programming problems and how to test the vertices.Several word problems and applications related to linear programming are presented along with their solutions and detailed explanations.Choose the scales so that the feasible region is shown fully within the grid.(if necessary, draft it out on a graph paper first.) Shade out all the unwanted regions and label the required region It also possible to test the vertices of the feasible region to find the minimum or maximum values, instead of using the linear objective function.It takes 4 hours to produce the parts of one unit of T2, 2.5 hour to assemble and 1.5 hours to polish.Per month, 7000 hours are available for producing the parts, 4000 hours for assembling the parts and 5500 hours for polishing the tables.Let x be the number of bags of food A and y the number of bags of food B.Cost C(x,y) = 10 x 12 y \[ \begin \ x \ge 0 \ \ y \ge 0 \ \ 40x 30y \ge 150 \ \ 20x 20y \ge 90 \ \ 10x 30y \ge 60 \ \end \] .Linear programming deals with this type of problems using inequalities and graphical solution method. She must buy at least 5 oranges and the number of oranges must be less than twice the number of peaches.An orange weighs 150 grams and a peach weighs 100 grams.

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