A gas processing plant receives unprocessed raw gas which it then converts into

Question

A gas processing plant receives unprocessed raw gas which it then converts into three grades of heating gas i.e. regular, premium and superior. The profit per ton for each grade of heating gas is given below The maximum amount of raw gas available for processing is 90 m3/week. Equipment availability is also limited to 80 hours/week. The storage for each product is also limited. Minimum of 1 ton of each product must be produced The goal is to find the optimal values of heating gas produced in tons per week. a) b) Classify the optimization problem and state the best MATLAB solver that can be used to the c) Formulate the optimization problem, stating clearly the objective function and all the constraints including the bounds. [12 points] problem. [3 points] Formulate the problem in a format that will allow you to solve it in MATLAB. [10 points]. DO NOI SOLVE Product Premium 10 Superior 4 Availability 90 (/week) 80 (hrs/week) Regular Unprocessed gas (m3/ton Processing time (hrs/ton) Storage (tons) Profit ($/ton) 15 150 10 180 170

Explanation / Answer

(a)Tons of Regular be x , Premium be y , Superior be z

Then 8x+10y+4z <= 90

Also 3x+5y+9z <= 80

And 1<= x <=15 , 1<=y<=7 , 1<=z<=10

Profit in dollars = 150x + 170y+180z

Objective :  max 150x + 170y+180z

(b) it is a maximization problem and we will use linprog solver to solve this problem

(c) x = linprog(f,A,b,Aeq,beq,lb,ub)

max 150x + 170y+180z = min -150x - 170y - 180z

f = [-150,-170,-180]

A = [8,10,4;3,5,9] (Note clearly comma and semi colon)

b = [90;80]

Aeq = []

b equ = []

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