In Exercises 1–4, find the value of the objective function at eac...

Question

In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=5x+6y

Graph showing a shaded region representing a system of inequalities with corner points labeled.

Accepted Answer

Welcome back. I am so glad you're here. We are given this objective function the equals two X plus four Y were asked to evaluate it at each corner of the graft region. So starting down here, we have the corner +34 and then working our way around, we have 48, The corner 77 and the corner 95. So what we'll do is plug the X and Y values for each of those corners in for X and Y in our objective function. And then once we've done that, we will determine the maximum and the minimum values. So let's plug in our first corner 34. So we'll have two times no longer X but now three plus four times no longer. Why? But now four, two times three is six plus four times four is 16 and six plus 16 is 22 right? The next corner 48, we'll have two times not X but four plus four times, not Y but eight, two times four is eight plus four times eight is 8 plus 32 equals 40. Now, the next .77. So we'll plug in seven for X and we'll plug in seven for Y two times seven is 14 plus four times seven is 28 14 plus 28 equals 42. And the last corner 95 will plug in nine for our X value and will plug in five for our Y value. Two times nine is 18 plus four times five is 20 and 18 plus 20 equals 38. Now, our maximum value, the highest one of 20 to 40 42 38 the highest one is 42 And our minimum value the lowest one that would be 22. Now, let's look at our answer choices and figure out which one matches. So at the 10.34, we're looking for a value of 22. Well, C is the only one that has that. Let's check the rest of C at 48. We're looking for a value of 40. We've got that at 77, a value of 42. We've got that at 95. We're looking for a value of 38. We've got that Maximum where Z is 42. Yup. And a minimum where Z is 22. We have that. All right. Answing choice. C works well done. We'll catch you on the next one.

In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=5x+6y

Key Concepts

Objective Function

Feasible Region

Corner Points

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