The ABC, Inc. is planning shipments of one of its products from two sources (A,B) to three destinations (I, II, III). Per unit transportation costs are given in the following table: (For example, it costs $3 per unit to ship from Source A to Destination I, and so on) The supplies for Source A and B are 140 units and 130 units respectively. The demands for Destination I, II, and III are 60 units, 90 units, and 110 units respectively. Let Xij denotes the units to ship from Source i to Destination j. where i=1 (Source A), 2 (Source B); and =1 (Destination I), 2 (Destination II), 3 (Destination III). 6% a) Based on the Excel output, write down the optimal shipment plan (i.e,, what is the optimal values for Xij,i=1,2;j=1,2,3) ? 2% b) Based on the optimal shipment plan in part a). What is the value of the objective function (i.e., the minimized total transportation costs)? 7% c) Based on the output, write down the range of optimality for the objective function coefficient of X12. Also, suppose the objective function coefficient of 12 is changed from $2 to $1. Do you think the optimal solution for Xij in part (a) will change or not? Explain your rationale. 7% d) Based on the output, write down the range of feasibility for constraint 3 (the demand of Destination I). Also, by how much the total tranportation costs in part b) will change if the demand of Destination I decrease from 60 to 50 ? Explain your rationale