Somewhere College allocates administrative costs to its teaching departments based on the number of students enrolled, while utilities are allocated based on the square feet of classrooms. The administrative costs for this period are $$400,000,$ and the utilities costs are $$200,000$ this period. Student enrollment and classroom size information for the four teaching departments follows:

$\backslash$table$[[$Teaching$\_$Department,$\frac{\text{S}\text{t}\text{u}\text{d}\text{e}\text{n}\text{t}\text{s}}{?},$Classroom Size$],[$Electronics$,117,900$ sq$,$ feet$],[$Automotive$,156,750$ sq$.$ feet$],[$Computers$,429,1,200$ sq$.$ feet$],[$Plumbing$,78,150$ sq$.$ feet$]]$

Required: Use the above information to allocate the administrative costs and utilities costs to the four teaching departments. $($Show allocation of the administrative costs in one set of calculations and allocation of the utilities costs in a separate set of calculations.$)(16$ points possible$)$