Linear Programming

King Fahd University of Petroleum & Minerals College of Industrial Management Second semester [phone]

CASE PROBLEM ( PRODUCT MIX) Prepared for DR Taqi Al-Faraj

Group J 225742 Bara'a Al-Jumbaz 4 226352 Mwuaffag Baswaid Ahmad Al-Abdul 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