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: Iron ore required Process type (tons/day) Coal required (tons/day) Labor required (person-days) Steel Produced (tons/day) Side products Produced (tons/day) 2 3 4 5 8 3 10 $50/ton 5 2 7 $10/ton 6 12 5 12 $150/person-day No limita- tions on availability of labor 4 6 2 6 $350/ton 4 $100/ton Cost Limitations 600 tons available per month 250 tons available per month All steel produced can be sold Only 200 tons can be sold per 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 profit, month b) Using the attached graph sheet attached at the end, please solve the following two separate LP problems graphically. i) Minimize fi(X) = 3x1 - 5x2 ii) Minimize f2(X) = 10x + 3x2, subject to the following constraints (for both problems): 6x1 + 5x2 > 30 8x1 + 2x2 > 16 3x1 + 5x2 > 15 X1, X2 > 0