Problem $4$

$(15$ marks$)$

A professor has been contacted by four not$-$for$-$profit agencies that are willing to work with student consulting teams. The agencies need help with such things as budgeting, information systems, coordinating volunteers, and forecasting. Although each of the four student teams could work with any of the agencies, the professor feels that there is a difference in the amount of time it would take each group to solve each problem. The professor's estimate of the time, in days, is given in the table below. Note that team $C$ is unable to help with coordinating volunteers. Formulate this assignment problem as a linear program.

$\backslash$table$[[$Projects$],[$Team$,$Budgeting,Information,Volunteers,Forecasting$],[$A$,32,35,15,27],[$B$,38,40,18,35],[$C$,41,42,-,38],[$D$,45,45,30,42]]$