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=40x+50y

Accepted Answer

Welcome back. I am so glad you're here. We are asked to evaluate the objective function which is Z equals 25 X plus 60 Y at each corner of the graft region. So our first corner we're going to look at is +00. The next corner we'll look at is 010. The next corner is 68 and the last corner we'll look at is 100 working our way around that graft region. And then we'll need to determine the maximum and the minimum value. So let's plug in our X and Y values from the corners for X and Y in our objective function. So for the first one will have 25 not times X but now zero plus 60 times no longer Y but now 25 times 00 and 60 times zero is zero and zero plus zero is zero. Now, the next corner we have 0 10 will be plugging in zero for the X value and we'll be plugging in 10 for the Y value. So 25 times zero is still zero plus 60 times 10 is 600 0 plus 600 is right now at 68 will be plugging in six for the X value and we'll be plugging in eight for the Y value 25 times six equals 60 times eight equals And 150 plus 480 equals 630. The last one will be plugging in 10 for the x value and we'll be plugging in zero for the Y value 25 times 10 is 250 plus 60 times zero is 0, 250 plus zero is 250. Right. Now, let's determine our maximum value. Looking at 0, 606 132 150. The maximum, the highest one is 630 and the minimum, the smallest one is zero. Now let's look at our answer choices and see which ones work. So at the 00.0, the value of Z is zero. Will that all of them work so far? Except for answer choice. B Now looking at the .010, we're looking for a value of 600. The only one that works there is answer choice. A. So let's check the rest of answer choice. A at 68, we have a value of 630. That's correct. At 10 0, we have a value of 250. That's correct. The maximum is where Z equals 630. Correct. And the minimum is where Z equals zero. Yes, that's what we got. All right. Answer. Choice. A 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=40x+50y

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