A small steel plant has available three processes For the pr

A small steel plant has available three processes For the production of steel. The processes require varying amounts of labor, ore, and coal and produce not only steel, hut also one side product with a limited saleability. The relevant data for an hour?s operation of each process is as follows.

Solution

Assumption:

Let labor = a; Ore = b; Coal = c;Steel = d; Side product = e & for processes Labor = a1, a2 & a3 and so on 1ton = 2000 LB

Constraint:

a1 + a2 + a3 <= 350 at $5.75/hr

b1 + b2 + b3 <= 5*2000 at $43/ton

c1 + c2 + c3 = max. at $150/ton

d1 + d2 + d3 <= 1

a1, a2, a3 <= 40

e1 + e2 + e3 <= 2000    S1 increment

e1 + e2 + e3 >= 2000    S2 increment

Maximize:

(150d1 + 125d2 + 185d3)*37/2000 + 35e1 + 15e2 + 75e3 - [ (8a1 + 11a2 + 7a3)*5.75 +(200b1 +140b2 + 300b3)*43/2000 + (145c1 + 120c2 + 225c3)*12/2000]                                   Subject to S1 & S2