I only need decision variables, constraints, and linear programming. Do not actually solve.

Also include two Additional Constraints: Plant 3 must not open if Plant 1 is open. Plant 5 opens only if its production level is at least half of its full capacity.

Formulate, do not solve.

Transportation Costs ($1,000) to Warehouse Annual Fixed Operating Cost From Plant 1 2 3 4 5 Annual Demand A $56 18 12 30 45 6,000 B $21 46 71 $32 7 41 61 26 8,000 D $65 35 52 28 31 10,000 Annual Production Capacity 12,000 18,000 14,000 10,000 16,000 $2,100,000 850,000 1,800,000 1,100,000 900,000 24 50 14,000