Find the value of the objective function z = 2x + 3y at each corn...

Question

Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function?

Accepted Answer

everyone in this problem. We are given a graft region and were asked to determine the value of the objective function. Z equals five X plus four Y. At each of the corners. Okay. We're asked to find the minimum and maximum values of that objective function. Okay. Alright so we see that we have the four corners. Okay, starting with this bottom left one which is 00. The bottom right is one. On the top right is and on the top left 0 13. Okay, so these are four corners. So these are the points that we want to evaluate the objective function at? Okay so let's start at 0 13 we have said is equal to five times X which is zero Plus four times y which is 13. This gives us zero plus 52. We had a value of 52. Alright, next point at and we have Z is equal to five times zero plus four times zero. This is just going to give us zero at 50. We have Z is equal to five times X. Which is five. So five times five plus four times Y. Four times zero we get 25 plus zero which gives us a value for our objective function of And for the last .4, we have Z is equal to five times X which is four plus four times Y. Which is five. So we get five times 4, 20 plus four times 5. 20 for a value of 40. Okay, alright so we found the value of our objective function at these corners. We know that the minimum and maximum will occur at these corners. Okay? So now it's just a matter of figuring out what the maximum and minimum value our that we found And so the maximum value we found. Well it was 52. Okay, that was the maximum value. We found that it occurred at 013 And the minimum value that we found, well that was zero and it occurred at 00. So our minimum value is zero. So our answer here is going to be c The minimum is zero and the maximum is 52. That's it for this one. Thanks everyone for watching. See you in the next video.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function?