See attached file for full problem descriptions with complete equations.

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1. During the next three months, Ironco faces the following demands for steel: 100 tons (month 1); 200 tons (month 2); 5 tons (month 3). During any month, a worker can produce up to 5 tons of steel. Each worker is paid $5000 per month. Workers can be hired or fired at a cost of $3000 per worker fired and $4000 per worker hired (it takes 0 time to hire a worker). The cost of holding a ton of steel in inventory for one month is $100. Demand may be backlogged at a cost of $70 per ton month. That is, if 1 ton of month 1 demand is met during month 3, then a backlogging cost of $140 is incurred. At the beginning of month 1, Ironco has 8 workers. During any month, at most 2 workers can be hired. All must be met by end of month 3. The raw material used to produce a ton of steel costs $300. Formulate an LP to minimize Ironco's costs.

2. The following LP is for a luxury cars and trucks Auto manufacture.

s.t.

In the above example, let c1 be the objective function coefficient of . Determine the optimal z-value as a function of c1.
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