formula a mathematics method to solve it - NO EXCEL please !

Problem 4. A small steel plant uses three processes for the production of steel. The processes require varying amounts of labor, ore, and coal and produce not only steel, but also one side product with limited salability. The relevant data for 1 hr of operation of each process is as follows. Input Labor Ore(lb) (worker-hours) 8 200 11 140 7 300 Process 1 Process 2 Process 3 Output Coal(b) Steel (lb) Side Products(lb) 145 550 35 120 735 15 225 600 75 For a week's operation the plant has available up to 5 tons of ore at $43/ton, 350 hr of labor at $15.75/hr, and an unlimited amount of coal at $12/ton. All the steel produced can be sold for $650/ton, and up to 1 ton of the side product can be sold for $37/ton (any amount above I ton has no value). Because of operational restrictions, no one process can be employed for more than 40 hr in any week. Determine (formulate LPP) an operating schedule that maximizes net income. (Suggestion. To incorporate the value of the production of the side product into the function to be optimized, divide its total amount produced into two increments, say S, and S2, where S, OS Si S 2000 lb represents the first ton produced.)