Question $2.$ Transportation Problem: Touche Young accounting firm has three auditors. Each auditor can work as many ds $160$ hours during the next month, during which time three projects must be completed. Project $1$ will take $130$ hours; project $2,140$ hours; and project $3,160$ hours. The amount per hour that can be billed for assigning each auditor to each project is given in Table $2.$

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Fall $2016$

a$.$ Formulate a linear programming model to maximize total billings during the next month.

b$.$ Find a feasible solution to the problem using Northwestern method. Suppose you solved the LP model in part a$.$ What do you expect when you compare it with the solution you found in this part?

Table $2$ Profits per Hour for Auditors on Projects

$\backslash$table$[[,$Profit per hour $($$$)],[,$Project $1,$Project $2,$Project $3],[$Auditor $1,120,150,190],[$Auditor $2,140,130,120],[$Auditor $3,160,140,150]]$