MIXED INTEGER LINEAR PROGRAMMING

MINIMISE = 5X₁₁+4X₁₂ + 6X₁₃ +6X₂₁ + 7X₂₂ + 3X₂₃

X11 +X12 + X3

X21 +X22 +X23

X11+X21>=300

X12 +X22>=350

X13 +X23>=250

Transportation Problem and Mixed Integer Linear Programming (MILP): The Company owns two factories in Southern California: one is in Pomona, while the other is in Riverside. The production capacities for Pomona factory (PF) and Riverside factory (RF) are 400 units and 500 units, respectively. The company also has 3 distribution centers, i.e., DC 1, DC 2, and DC 3. (10 points) The demands for DC 1, DC 2, and DC 3 are 300 units, 350 units, and 250 units, respectively. It turns out the transportation costs (per unit) from PF to DC 1, DC 2, and DC 3 are $5, $4, and $6, respectively. And the transportation cost (per unit) from RF to DC I, DC 2, and DC 3 are $6, $7, and $3, respectively. All the information is summarized into the following table. The company would like to minimize the total transportation cost to deliver the units from factories to distribution centers. Please help the company to formulate the problem as a mixed integer linear programming, where the objective function and constraints are linear function, and the decision variables may be integers (hint: you can define the number of units transported from one factory to another distribution center as decision variables). Due to the scarcity of raw materials, the production of both factories has been reduced by 10%. However, the demand is not changed. Is there a feasible solution to this problem? Please explain *(+)* TC17 trend of the eaus. @ DO2 DC3 min :- 5x + 4X2 + 6x13. + 6X2 + 7X22. + 3X23 sit. Xin + Xiz+X,3 250 Xi & Boject & HCM (Highway Manue) L Capacity a Ureeway se Capacity Service desind TITITITILL VLLOL thase Contro Device. amps "X CC 009 oog soolt " 009 no BE aas Slot 00860 aobs Co1 048 = 08+0000 0.75 4800 Gov. 5400 OLTO SLOT e#2 SECH