00:01
Hello everyone, we need to find the number of pancakes and danish produce each day to maximize the profit.
00:07
So let us take the decision variables, that is, number of pans of coffee cakes is equal to x1.
00:24
And let the number of pans of danish be equal to x2.
00:33
So the maximize profit function be z is equal to 6x1.
00:38
Plus 12 x2 so the constraints will be 4 x1 plus 5 x2 less equal to 25 2 x1 plus 4 x2 less equal to 16 and x1 less equal to 6 and we have x1 x2 greater than or equal to 0 so the graph of these constraints is shown here now let us evaluate the maximum profit by substituting the plotted points.
01:16
That is, at the point 0 .0, the maximum profit z will be 0.
01:28
At the point 0 .5, the maximum profit z will be 60.
01:36
Similarly for other points we can calculate that is for 0 .4 we have 48 as the maximum profit.
01:48
Similarly at the point 6 .0 we have z to be equal to 36.
01:58
Similarly at the point 8 .0 the maximum profit is 48 and at the point 3 .33 and at the point 3 .33 .2 the maximum profit z is 47 .99 so clearly from this we can see that the maximum profit value is dollar 60 and it occurs at the point 0 .5 so clearly from this we can answer our questions that is in part a we need to find the number of kicks so the maximum profit occurs at the point 0 .5, we have x1 is equal to 0...