## Linear Programming (Graphical Method)

Graphical Method of Solving Linear Programming Problems. We already know how to plot the graph of any linear equation in two variables. The process involves plotting the points that satisfy the equation on the coordinate axis and joining them. COPYRIGHT © by LAVON B. PAGE Michigan Polar Products makes downhill and cross-country skis. A pair of downhill skis requires 2 man-hours for cutting, 1 man-hour. Section – Solving Linear Programming Problems There are times when we want to know the maximum or minimum value of a function, subject to certain conditions. An objective function is a linear function in two or more variables that is to be optimized (maximized or minimized).

## Graphical Method of Solving Linear Programming Problems

Within this context we will present a series of Linear Programming exercises that have been solved using the graphical method. Exercise 1: A workshop has three 3 types of machines A, B and C; it can manufacture two 2 products 1 and 2, and all products have to go to each machine and each one goes in the same order; First to the machine A, then to B and then to C.

The following table shows:. Formulate and solve using the graphical method a Linear Programming model for the previous situation that allows the workshop to obtain maximum gains, solving linear programming problems graphically.

The constraints represent the number of hours available weekly for machines A, B and C, respectively, solving linear programming problems graphically also incorporate the non-negativity conditions. The green colored area corresponds to the set of feasible solutions and the level curve of the objective function that passes by the optimal vertex is shown with a red dotted line.

Exercise 2: A winemaking company has recently acquired a hectares piece of land. You want to know how to plant each variety in the hectares, given the costs, net profits and labor requirements according to the data shown below:. Formulate and solve graphically a Linear Programming model for this problem.

Clearly outline the domain of feasible solutions and the process used to find the optimal solution and the optimal value. Where the restrictions are associated with the maximum availability of hectares for planting, available budget, man-hours in the planting period and non-negativity, solving linear programming problems graphically, respectively.

The following graph shows the representation of the winemaking company problem. The shaded area corresponds with the domain of feasible solutions, where the optimal basic feasible solution is reached at vertex C, where the budget and man-days restraints are active.

Exercise 3: A company produces two different products. Given the current availability of staff in the company, each day there is at most a total of solving linear programming problems graphically hours available for assembly and 80 hours for quality control.

In addition, the maximum amount of daily sales for the first product is estimated to be units, without there being a maximum limit of daily sales for the second product. Formulate and solve graphically a Linear Programming model that will allow the company to maximize profits.

The first constraint represents the daily assembly time constraints. The second constraint is the availability of time for quality control also daily. The third constraint establishes an upper bound for the manufacturing and daily sales of Product 1. In addition, the non-negativity conditions for the decision variables are included. Name required, solving linear programming problems graphically. Email will not be published required. This site uses Akismet to reduce spam.

Learn how your comment data is processed. Rate this item: 1. Please wait How to Calculate the Shadow Price of a Constraint. Manish Kaushik November 25, en am. Masroaf Shahrin August 29, en am. These exercises with solution have helped me a lot…!

### a. Solving Linear Programming Problems Graphically | Finite Math Oct 13,  · The Graphical Method (graphic solving) is an excellent alternative for the representation and solving of Linear Programming models that have two decision erlreds.gq this purpose there are computational tools that assist in applying the graphical model, like TORA, IORTutorial and Geogebra.. Within this context we will present a series of Linear Programming exercises that have been solved /5(8). Graphical Method of Solving Linear Programming Problems. We already know how to plot the graph of any linear equation in two variables. The process involves plotting the points that satisfy the equation on the coordinate axis and joining them. Solving Linear Programming Problems Graphically (This topic is also in Section in the most recent edition (6e) of Finite Mathematics and Section in the most recent edition (6e) of Finite Mathematics and Applied Calculus). Online resource for this topic: Online: Linear programming grapher | Get the app.