iic optilal pon 4. a) Formulate the following optimization problem as a LP probl

ID: 426439 • Letter: I

Question

iic optilal pon 4. a) Formulate the following optimization problem as a LP problem. Please do not s A steel plant produces steel using four different types of processes. The i and labor required, the amounts of steel and side products produced, the cost into and the physical limitations on the system are given below: ron ore, coal, Iron ore required required Labor required Produced Side products Produced Coal Steel Process type (tons/day) (tons/day)(person-days) (tons/day)(tons/day) 2 12 4 12 4 Cost $50/ton S10/ion $150/person-day $350/ton 100/ton Limitations 600 tons 250 tons No limita- All steel Only 200 available per month available per month tions on availability of labor produced can be sold 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 profity monlh

Explanation / Answer

Decision Variables: Let a,b,c & d represent the number of days the four different processes (1,2,3 & 4) are used in a month respectively.

Objective Function: Maximize Profit

Profit= Sales-Cost

Sales = (4a+6b+2c+6d)*320 + (a+2b+c+4d)*100

Costs = (5a+8b+3c+10d)*50 + (3a+5b+2c+7d)*10+ (6a+12b+5c+12d)*150

Constraints:

a,b,c,d>=0,int

(no of days cannot be in-fractions)

a+b+c+d=30

(no of days/month)

5a+8b+3c+10d<=600

iron ore availability

3a+5b+2c+7d<=250

coal availability

a+2b+c+4d<=200

Max. side product that can be sold