A manufacturer makes two types of rubber, Butadiene and Polyisoprene. The plant

Question

A manufacturer makes two types of rubber, Butadiene and Polyisoprene. The plant has two machines, Machine-1 and Machine-2, and both of them are used to make the rubber strips. Machine-1 is available 180 hours per month and Machine-2 is available 200 hours per month. Manufacturing one strip of Butadiene requires 2.75 hours on Machine-1 and 3 hours on Machine-2. For processing one strip of Polyisoprene, it takes 3.5 hours on Machine-1 and 4 hours on Machine-2.

a. Formulate an all-integer model that will determine how many units of each type of the rubber should be used to maximize the manufacturer’s contribution to profit if he gets a profit of $20 on Butadiene and $26 on Polyisoprene?

b. Use Excel Solver to determine the optimal number of units produced of each type of rubber (Butadiene and Polyisoprene).

Explanation / Answer

Answer:

Problem is

Entering =X2=X2, Departing =S2=S2, Key Element = 44

R2R2 (new) =R2=R2 (old) ÷4=R2÷4=R2 (old) 1414

R1R1 (new) =R1=R1 (old) 3.5R2-3.5R2 (new)

Entering =X1=X1, Departing =S1=S1, Key Element = 0.1250.125

R1R1 (new) =R1=R1 (old) ÷0.125=R1÷0.125=R1 (old) 88

R2R2 (new) =R2=R2 (old) 34R1-34R1 (new)

Since all CjZj0Cj-Zj0,

Optimum Solution is arrived with value of variables as :
X1=40

X2=20

Maximise Z=1320

MAX Z=Z= 2020 X1+X1+ 2626 X2X2 Subject to constraints 2.752.75 X1+X1+ 3.53.5 X2X2 180180 33 X1+X1+ 44 X2X2 200200 and X1,X20X1,X20

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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