The Texas Consolidated Electronics Company is considering an R&D program encompassing eight research projects.

In the model for this problem Xi is a $0-1$ variable for the selection of project i$,$ where i $=1$ to $8.$

One of the conditions in the modified model is that the same decision be applied to project $2$ and project $5.$ If project $2$ is selected then project $5$ is selected. And if project $2$ is not selected then project $5$ is not selected.

So$,$ modify the constraint on decision variables x$2$ and x$5$ to represent this updated condition. Leave the other constraints $($budget and personnel$)$ the same. Then answer the following question.

Which projects are selected?

The Texas Consolidated Electronics Company is considering an R&D program encompassing eight research projects.

In the model for this problem Xi is a $0-1$ variable for the selection of project i$,$ where i $=1$ to $8.$

One of the conditions in the modified model for this problem is that either project $2$ or project $5$ must be selected but not both of them.

So$,$ modify the constraint on decision variables x$2$ and x$5$ to represent this updated condition. Leave the other constraints $($budget and personnel$)$ the same. Then answer the following question.

What is the value of the objective function at the updated solution?