a) Formulate the following optimization problem as a LP problem. Please do not solve it. A steel plant produces steel using four different types of processes. The iron ore, coal. and labor required, the amounts of steel and side products produced, the cost information, and the physical limitations on the system are given below: Side products required required Labor required Produced Produced Process type (tons/day) (tons/day) (person-days) (tons/day) (tons/day) Iron ore Coal Steel 4 2 12 12 4 10 $50/ton 4 Cost S10/ton SI50/person-day $350/ton S100/ton Limitations 600 tons 250 tons No limita- All steel Only 200 produced can be sold tions on available per month tons can be sold per month available availability of labor month Assume that a particular process can be employed for any number of days in a 30-day month, determine the operating schedule of the plant for maximizing the profity manth