# Quiz 5: Decision Making

Linear programming model is used to obtain maximum profits, by utilizing minimum resources available. It helps the decision makers to take effective decisions by using the resources productively. It helps in minimizing cost of operations. It consists of objective function, model constraints and decision variables. Formulate the LPP to solve this problem graphically, first use the following constraint equations and plot a graph. The first equation represents the painting constraint. There is a total of 80 hours of painting available from the two painters in one week. The two variable b and t represent the number of blocks and trucks produced, respectively. The second equation represents the wood working constraint. Construct a graph using the following methodology as explained below: Consider B as x and T as Y for the coordinate calculation. Calculate coordinates for equation (1) as shown below: Step: 1 Calculate the coordinates for the equation (1) by assuming the value of y=0 shown as follows: Calculate the coordinates for the equation (1) by assuming the value of x=0 shown as follows: Therefore, the coordinates for the equation (1) are (40, 0) and (0,80). Calculate coordinates for equation (2) as shown below: Step: 1 Calculate the coordinates for the equation (2) by assuming the value of y=0 shown as follows: Calculate the coordinates for the equation (2) by assuming the value of x=0 shown as follows: Therefore, the coordinates for the equation (1) are (120, 0) and (0,40). Construct a graph by using the above coordinates as shown below:  From the above graph, it can be identified that points O, D and B are in the feasible region. Notice the green region having coordinates of x 1 =24 and x 2 = 32, which satisfies the objective function as follows: Substitute the values of x 1 and x 2 in the objective function as shown below: Therefore, from the above graphical analysis it indicates that the optimal number of blocks is 24 , and the optimal number of trucks is 32. Solving the system of equations will give the same result.