00:01
In this problem we need to solve the linear programming problem and we have the objective function maximize z is equal to 18x plus 7y and it is subjected to constraints 2x plus 8y less than equals to 16 9x plus y less than equals to 16 and we have the non -negative restrictions x 3x greater than equals to 0 and y greater than equals to 0.
00:36
First of all, let's draw the corresponding graph to these equations to x plus 8y less than equals to 16 and 9x plus y less than equals to 16.
00:47
So substitute y is equal to 0 in this equation 2x plus 8y less than equals to 16.
00:57
So we get x is equal to 8 so we can say that this line passes through the point 8 comma 0 now substitute x is equal to 0 so we get y is equal to 2 so we can say this line passes through the point 0 comma 2 similarly now let's consider this equation 9x plus y less than equals to 16 so when we substitute y is equal to 0, we get x is equal to 16 over 9.
01:35
So we can say this line passes through the point 16 over 9 comma 0.
01:41
And when we substitute x is equals to 0, we get y is equals to 16 or we can say this line passes through the point 0 .16.
01:52
Now let's draw these graphs on the graph paper and the lines of the lines of the on the graph paper are shown below.
02:03
So here we have the graph corresponding to given equations.
02:07
This red line represents 2x plus 8y less than equals to 16 and this blue line represents 9x plus y less than equals to 16.
02:23
Now since we have the less than or equals to sign, therefore we can say that the feasible reason lies below these lines and this is the common visible region and from the graph we have the coordinates 0 .2 0 .0 and 1 .778 .0 or we can say 16 over 9 .0 and when we solve the equations of these two lines we get the coordinate of this point which are 1 .6 .1 .6 now let's substitute all these values in the objective function...