I've managed to fix my problem as all I had to do was build the package on Visual Studio BIDS, by right clicking the project on the Solution Explorer on the right hand side and selecting
Properties. I then clicked on Deployment Utility on the pop-up window and set the CreateDeploymentUtilityto True. I then clicked OK.
I then right clicked on the project in the Solution Explorer again and clicked on
Build in the pop-up drop-down menu.
After it was successfully built, I logged in to the Integration Services server on SQL Server Management Studio, and then navigated to
Stored Packages > File System in the Object Explorer and right clicked on File System and clicked Import Package.
In the pop-up window I selected
File System in the Package location field, and browsed and selected the built package located in the my project folder\bin\Deployment. I left the Package name field as the same as the original package and then overwrote the original package after clicking OK in the window.