Grade 4: OR Section Term 2 Section 4 Linear Programming applications (1) Youtube: https://youtu.be/Pan9ETHb_3U

1. By:
Zakaria Elsayed Hasaneen
Teaching Assistant at Faculty of Commerce
Accounting Department (English Section)
Kafrelsheikh University
OR
Section (4)
Linear Progamming applications (1)
Grade 4 –Term 2
Zakaria Hasaneen
Zakaria Hasaneen
Zakaria Hasaneen

2. ZIKO Foods manufactures a snack mix called ZAK by blending three
ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture.
Information about the three ingredients (per ounce) is shown below:
Blending Problem

3. The company needs to develop a linear programming model whose
solution would tell them how many ounces of each mix to put into
the ZAK blend. ZAK is packaged in boxes that will hold between
three and four cups. The blend should contain no more than 1100
calories and at most 30 grams of fat. Dried fruit must be at least
30% of the volume of the mixture, and nuts must be no more than
25% of the weight of the mixture.
Let:-
x = amount (ounces) of dried fruit to put into ZAK.
y= amount(ounces) of nut mix to put into ZAK.
z= amount (ounces) of cereal mix to put into ZAK.

4. (1) What is the objective function?
A) max0.4x+0.5y+0.2z
B) max0.25x+0.5y+z
C) min0.4x+0.5y+0.2z
D) min0.25x+0.5y+z
E) None of the above
ANS: Given Information:
We have to develop a model that meets the restrictions given
to minimize the cost of the blend.
The Objective function of Linear Programming Problem is given
by:
MinZ=0.4x+0.5y+0.2z
Hence, option (C) is the correct answer.

5. (2) What is the constraint for calories?
A)150x+400y+50z≥1100
B)150x+400y+50z≤1100
C) x+y+z≥1100
D) x+y+z≤1100
E) None of the above
ANS: The blend should contain no more than 1100 calories that
is the maximum amount of calories blend can contain is 1100
The constraint for calories is:
150x+400y+50z≤1100
Hence, option (B) is the correct answer.

6. (3) What is the constraint for fat?
A) x+y+z≥30
B) x+y+z≤30
C)15y+3z≥30
D)15y+3z≤30
E) None of the above
ANS: The blend should contain at most 30 grams of fat.
The constraint for fat is:
0x+15y+3z≤30
15y+3z≤30
Hence, option (D) is the correct answer.

7. (4) What is the volume constraint for dried fruit?
A) −0.7x+0.3y−0.7z≥0
B) 0.3x−0.7y+0.3z≥0
C) 0.21x−0.15y−0.3z≤0
D) 0.21x−0.15y−0.3z≥0
E) None of the above
ANS: The Dried fruit must be at least 30% of the volume of the
mixture.
The volume constraint for dried fruit is:
x≥0.3(0.3x+0.5y+1z)
x≥0.09x+0.15y+0.3z
0.91x−0.15y−0.3z≥0
Hence, option (E) is the correct answer.

8. (5) What is the weight constraint for nut mix?
A) 0.25x−y−z≤0
B) 0.75x−0.25y−0.25z≤0
C) x−0.25y−0.25z≤0
D)−0.25x+0.75y−0.25z≤0
E) None of the above
ANS: Nuts must be no more than 25% of the weight of the
mixture.
y≤0.25(0.3x+0.5y+1z)
0.075x−0.8750y+0.25z≥0
Hence, option (E) is the correct answer.

9. An ad campaign for a new snack chip will be conducted in a
limited geographical area and can use TV time, radio time, and
newspaper ads.
Information about each medium is shown below.
If the number of TV ads cannot exceed the number of radio ads by
more than 4, and if the advertising budget is $10000.
Media selection
Required: Develop the model that will maximize the number reached and
achieve an exposure quality if at least 1000.

10. ANS:
Let T = the number of TV ads
Let R = the number of radio ads
Let N = the number of newspaper ads
Max 10000T + 3000R + 5000N
s.t. 500T + 200R + 400N ≤ 10000
30T + 40R + 25N ≥ 1000
T − R ≤ 4
T, R, N ≥ 0