Hi guys positive rating to whoever answers this question in detail! thankks for

Question

Hi guys positive rating to whoever answers this question in detail! thankks for your help!

An oil refinery has available three different processes to produce gasoline. Each process produces varying amounts of three grades of gasoline: regular, low-lead, and premium. These amounts in hundreds of gallons per hour of operation, are given in the following table, along with the cost in dollars of an hour's operation of each of the processes. The refinery must meet the weekly demands of 1500 gal of regular, 3000 gal of low-lead and 1000 gal of premium. Furthermore, for market reasons, the weekly production of low-lead should at least twice as much as the weekly production of regular, and at least three times the weekly production of premium. Set up the cost minimization problem as a linear programming problem, defining the decision variables clearly.

Explanation / Answer

let xij represent from process i and type j

i = 1 , 2 , 3 and j = 1 for regular , 2 for low-lead , 3 for premium

for eg. x23 represent hours from process 2 to produce premium

now we have minimize

Z = 160(x11+ x12 +x13) + 400*(x21+x22 +x33) + 600*(x31 +x32+x33)

now constraint

from demand

x11 + 6*x21 + 6*x31 >= 1500   

5*x12 +6* x22 +3* x33 > = 3000

x13 + 8*x23 + 2*x33 >= 1000

for market reasons

5*x12 +6* x22 +3* x33 >= 2 *(x11 + 6*x21 + 6*x31)

x11 + 6*x21 + 6*x31 >= 3*(x13 + 8*x23 + 2*x33 )

Please rate my solution

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.