Tri-State Manufacturing has three factories (1, 2, and 3) and three warehouses (A, B, and C). The following table shows the shipping costs between each factory and warehouse, the factory manufacturing capabilities (in thousands), and the warehouse capacities (in thousands). Management would like to keep the warehouses filled to capacity in order to generate demand. FROM/TO WAREHOUSE A WAREHOUSE B WAREHOUSE C PRODUCTION CAPACITY Factory 1 $4 $7 $3 6 Factory 2 $8 $12 $8 9 Factory 3 $10 $16 $16 12 Capacity 8 14 5 (3 points) Formulate this as a linear programming problem (write out the objective function and the constraints including non-negativity constraint, use decision variables like X1A for 1,000s of units shipped from factory 1 to warehouse A, and so on). (3 points) Solve this problem using the corner-point method or the iso-profit/iso-cost line method, giving the optimal values of all variables (3 points) What is the total cost of transportation? (2 points) Which constraints are binding? 3 points bonus if you solve the question using Excel OM. 5 points bonus Solve the same problem using excels solver using "Simplex LP" instead of the default solver "GRG nonlinear" running a sensitivity analysis and explain the shadow prices.