Decision Science 1, Computer Practical,
Practical work, Week 4 P4 Pair number: 14
Name: Lars van der Horst Studentnumber: 1 0 4 9 5 2 8
Name: Dennis van den Berg Studentnumber: 1 0 4 8 1 6 8
Watch the Introduction clip to practical P4
Exercise 7
The next questions are all related to exercise 7 of your syllabus (blending
problem).
You already formulated the general LP-model at home (exercise 7b).
7-c/d Open the existing file << DS1_07 Multi blend.mos >>. Translate the model formulation you found in
exercise b. into the syntax of Xpress-IVE such that the problem can be solved in Xpress-IVE.
Give the model formulation. You can either use the formula editor, or write your model on paper and
insert a picture of it here. Note: if you managed to make a flawless model in your homework, you can
copy that model here.
Demand:
X11 + X21 + X31 + X41 + X51 >=1000 Som i Xij>=Dj for all j
X12 + X22 + X32 + X42 + X52 >=1500
X13 + X23 + X33 + X43 + X53 >=500
J: X1j + X2j …..........................>= Dj
Stock:
X11 + X12 + X13 <= 400 Som j Xij<=Sl for all i
.
.
X51 + X52 + X53 <= 300
Starch:
0,8*X11+0,62*X21+0,65*X31+0,75*X41+0,68*X51 Som I PS*Xij >= Rs for all j
Minamount
Xij => Minamountij Som ij Xij => Minamountij For all I,j
X11 => 0
Objective function
Min(TC=0,40*X11+0,40*X22.........+1,35*X53) Min(TC=som Ci*Xij)
Give the solution of the problem.
kg Final product 1 Final product 2 Final product 3
Raw material 1 350 0 50
Raw material 2 400 600 125
Raw material 3 100 250 325
Raw material 4 0 500 0
Raw material 5 150 150 0
Objective function value = 3637.5
Suppose (!) you want to solve the problem in exercise 7d. manually; so producing three final products
(j=1,2,3) with five different raw-materials (i=1,2,3,4,5).
7-e Do you need to apply the two-phase method? (Argue your answer!)
Yes, in the constraints with >= you get a – Y. If you put this in the simplex tableaus, you don't have a
unit matrix. So you have to add Z to get the unit matrix. Then you have to get rid of the Z in phase I
Practical work, Week 4 P4 Pair number: 14
Name: Lars van der Horst Studentnumber: 1 0 4 9 5 2 8
Name: Dennis van den Berg Studentnumber: 1 0 4 8 1 6 8
Watch the Introduction clip to practical P4
Exercise 7
The next questions are all related to exercise 7 of your syllabus (blending
problem).
You already formulated the general LP-model at home (exercise 7b).
7-c/d Open the existing file << DS1_07 Multi blend.mos >>. Translate the model formulation you found in
exercise b. into the syntax of Xpress-IVE such that the problem can be solved in Xpress-IVE.
Give the model formulation. You can either use the formula editor, or write your model on paper and
insert a picture of it here. Note: if you managed to make a flawless model in your homework, you can
copy that model here.
Demand:
X11 + X21 + X31 + X41 + X51 >=1000 Som i Xij>=Dj for all j
X12 + X22 + X32 + X42 + X52 >=1500
X13 + X23 + X33 + X43 + X53 >=500
J: X1j + X2j …..........................>= Dj
Stock:
X11 + X12 + X13 <= 400 Som j Xij<=Sl for all i
.
.
X51 + X52 + X53 <= 300
Starch:
0,8*X11+0,62*X21+0,65*X31+0,75*X41+0,68*X51 Som I PS*Xij >= Rs for all j
Minamount
Xij => Minamountij Som ij Xij => Minamountij For all I,j
X11 => 0
Objective function
Min(TC=0,40*X11+0,40*X22.........+1,35*X53) Min(TC=som Ci*Xij)
Give the solution of the problem.
kg Final product 1 Final product 2 Final product 3
Raw material 1 350 0 50
Raw material 2 400 600 125
Raw material 3 100 250 325
Raw material 4 0 500 0
Raw material 5 150 150 0
Objective function value = 3637.5
Suppose (!) you want to solve the problem in exercise 7d. manually; so producing three final products
(j=1,2,3) with five different raw-materials (i=1,2,3,4,5).
7-e Do you need to apply the two-phase method? (Argue your answer!)
Yes, in the constraints with >= you get a – Y. If you put this in the simplex tableaus, you don't have a
unit matrix. So you have to add Z to get the unit matrix. Then you have to get rid of the Z in phase I
