Find the maximum and minimum values of each objective function ov...

Question

Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right.  objective function = 10y

Accepted Answer

Welcome back. I am so glad you're here. We are asked to evaluate the objective function Z at the vertices of the graph of the region of feasible solutions and determine the maximum and minimum values of the function. Our function is Z equals Y. And then we have a graph which shows a shape. It has vertices at 29, 10, 11, 10, 1 and answer choice. A gives us a maximum of 126 and a minimum of answer. Choice B has a maximum of 104 and a minimum of answer choice C has a maximum of 154 and a minimum of 14. And answer choice D has a maximum of 96 and a minimum of 42. Now to solve for our objective function, what we need to do is put the X and Y values. Remember from previous lessons when we have an ordered pair, the X value comes first followed by the Y value. We plug the X values in for X in our function and we plug the Y values in for Y in our objective function. The one that Z is equal to and then we solve and the highest numbers are maximum, the lowest numbers are minimum. Now, what's interesting about this is that RZ only has a Y value. It doesn't have a place for X. There are zero XS. So we'll just be plugging in the Y values. So for that first ordered pair, we had 29, the Y value is nine. So we're plugging nine in for Y, we have 14 multiplied by nine, that equals 126. Now, for the next vertex, we have the ordered pair. 10, 11, the Y value is 11. So we're plugging in 11 for Y, we have 14 multiplied by 11, that equals 154. Now for our next ordered pair, the next vertex we have 10, 1, our Y value is one. So we're plugging one in for Y, we have 14 multiplied by one that equals 14. Now for our final vertex at the 0.43 the Y value is three, plugging three in for Y, we have 14 multiplied by three that equals 42. So again, that highest value is our maximum. The highest value here is 154 and the lowest value is our minimum. Our minimum here is 14. So we look at our answer choices for a maximum of 154 and a minimum of 14. And that matches with answer choice. C well done. We'll catch you on the next one.

Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. objective function = 10y

Key Concepts

Objective Function

Feasible Region

Linear Programming

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