 Hi and how are you all today? The question says solve the following linear programming problem graphically. Here we need to maximize z that is equal to 60x plus 15y subject to the constraint x plus y is less than equal to 50. 3x plus y is less than equal to 90 and both the values of x and y are greater than equal to 0. So let us proceed with the solution. Now first of all let us convert the given inequalities into equations. So we have x plus y equal to 50 and the second one as 3x plus y is equal to 90. Now we need to find out two points for each equation. For this one when x is 0, y is 50 and when y is 0 the value of x comes out to be 50. Now for this one we have it as when the value of y is 0 then the value of x is 30 and when the value of x is 0 then the value of y is 90. So let us plot these two equations on the graph. Now it is given to us that both the value of x and y is greater than equal to 0 so we will be considering the first quadrant itself. Now we will be plotting the points on the graph. We have when x is 0 then y is 50 then it must be here and when y is 0 x is also 50. Now let us join these two points to obtain the point which represents the equation x plus y is equal to 50. Now we have the next equation as 30 0 so this is the point 30 0 and then we have the next point as 0 90. Now this is the line representing the equation 3x plus y is equal to 90. Now they are intersecting at this point let's say p where the value of x is 20 and y is 30. So we can write that first of all let us find out the profit function that is the function which we need to maximize it can be any function. We are given here the points which we will be taking are and this is the point p20 13 which we need to see what will be the maximum value of z that is 16 into 20 plus 15 into 30. That gives us 1200 plus 450 in turn giving us 1650. So here when the value of x is 20 and y is 30 that will give us the maximum value of z when x is equal to 20 and y is equal to 30. So this completes this session hope you understood it well have a nice day.