Consider the following transportation problem. Suppose that any shortage in meeting demand of construction sites results in penalty costs of 11, 9 and 7, respectively. Construction Site 3 Plant 1 $8 59 1 2 2 $6 Supply 125 175 200 $9 $11 $11 3 $12 $5 $12 Demand 200 100 300 a) Write out the Linear Programming model for the problem. (5 Points) b) Calculate total cost using least cost method for the problem. (5 Points) c) Find the optimal solution using method of multipliers and calculate total cost. (10 Points) d) Interpret the solution in (c). (5 Points) e) Write out Lingo code using sets to get optimal solution. (10 Points)