CASE PROBLEM ( PRODUCT MIX) Prepared for DR Taqi AlFaraj
Group J 225742 Bara'a AlJumbaz 4 226352 Mwuaffag Baswaid Ahmad AlAbdul Muney" 205943
30 May 2006
Case Problem PRODUCT MIX
Background:
TJ's Inc., makes 3 nut mixes for sale to grocery chains located in the Southeast. The three mixes are: Regular Mix, Deluxe Mix and Holding Mix. They are made by mixing different percentages of five types of nuts as follow:
Regular Mix Deluxe Mix Holding Mix
Almond 15% 20% 25%
Brazil 25% 20% 15%
Filbert 25% 20% 15%
Pecan 10% 20% 25%
Walnut 25% 20% 20%
TJ's has just purchased the following shipments of nuts at the prices shown: Type of Nut Shipment Cost per Shipments($) Amount(Pounds) Almond 6000 7500 I I Brazil 7500 7125 Filbert 6750 7500 Pecan 6000 7200 7875 Walnut 7500
I
1
The ~ r o f icontribution Der Pound and Customer orders are: t Profit contribution per Pound Customer Orders (Pounds) Regular mix $1.65 10000 Deluxe mix $2 3000 Holding Mix $ 2.25 5000
Solution:
Xij = quantity of nut (i) to mix j i= 1,2,3,4,5 j= 1,2,3 Profit
1$1.65
I $2.00
D
I $2.25
H
X13
R A
F P

Available
6,000 pounds
I
I
I
XI1 X21
I
I
I
X12 X22
I X23
I X33
1 7,500 pounds I
1 7,500 pounds 1 6,000 pounds
I
I
w
Max s.t.
I X51
I X31 I X41
I X32 I X42
Orders
I 10.000 pounds
I X52
I X43 I X53
I
I
I
( 3.000 pounds
1 5,000 pounds
1 7,500 pounds
1.65(Xll+X21+X3 1+X41+X51) + 2(X12+X22+X32+X42+X52) + 2.25(Xl3+X23+X33+X43+X53) X1 l+X12+X1316,000 X2 1+X22+X2317,500 X3 1+XX?+X3317,5OO X4 1+X42+X4316,000 X5 1+X52+X5317,5OO 0.15X11+0.25X21+0.25X31+0.10X41+0.25X51>10,000 0.20X12+0.20x22+0.20X32+0.20x42+0.20X52>3,000 0.25X13+0.15X23+0.15X33+0.25X43+0.20X53>5,000 Xij>O for all ij
1 Cost per pound of the nuts ( cost per shipmentslshipments Amount)
I Almond
Brazil Filbert