A company sells sets of kitchen knoves. The basic set consists of utility knives
ID: 3143194 • Letter: A
Question
A company sells sets of kitchen knoves. The basic set consists of utility knives and 1 chefs knife. The regular set consists of 2 utility knives, 1 chefs knife and 1 slicer. The deluxe set consists of 3 utility knives, 1 chefs knife, and 1 slicer. The profit is $30 on the basic, $40 on the regular, and $60 on the deluxe set. the company has on hand 800 utility knives, 400 chefs knives and 200 slicers.
a. How many sets of each type should be made up and sold in order to maximize profit?
b. What is the maximum profit?
APPROACH:
- Clearly state the objective function and constraints of the linear programming
-State the initial simplex tableau
- State the final simplex tableau
-Answer the questions asked.
Explanation / Answer
The Cut-right company sells sets of kitchen knives. The Basic Set consists of 2 utility knives and 1 chef's knife. The Regular Set consists of 2 utility knifes, 1 chef's knife, and 1 slicer. The Deluxe set consists of 3 utility knives, 1 chef's knife and 1 slicer. The profit is $30 on a basic set, $40 on a Regular set, and $60 on a Deluxe set. The factory has on hand 800 utility knives, 400 chef's knives, and 200 slicers. assuming that all sets will be sold, how many of each type should be made up in order to maximize profit? what is the maximum profit?
Formulation of the LPP
For maximum profit, let the number of sets to be sold be x of the Basic type, y of the Regular type and z of the Deluxe type.
Maximize P = 30x + 40y + 60z subject to
2x + 2y + 3z 800 (Utility knives constraint)
x + y + z 400 (Chefs knives constraint)
y + z 200 (Slicers constraint)
x, y, z 0
Tableau #1
x
y
z
s1
s2
s3
p
2
2
3
1
0
0
0
800
1
1
1
0
1
0
0
400
0
1
1
0
0
1
0
200
-30
-40
-60
0
0
0
1
0
Tableau #2
x
y
z
s1
s2
s3
p
2
-1
0
1
0
-3
0
200
1
0
0
0
1
-1
0
200
0
1
1
0
0
1
0
200
-30
20
0
0
0
60
1
12000
Tableau #3
x
y
z
s1
s2
s3
p
1
-0.5
0
0.5
0
-1.5
0
100
0
0.5
0
-0.5
1
0.5
0
100
0
1
1
0
0
1
0
200
0
5
0
15
0
15
1
15000
The optimum solution is x = 100 (Basic Type), y = 0 (Regular Type), z = 200 (Deluxe Type) and profit, P = $15000.
The Cut-right company sells sets of kitchen knives. The Basic Set consists of 2 utility knives and 1 chef's knife. The Regular Set consists of 2 utility knifes, 1 chef's knife, and 1 slicer. The Deluxe set consists of 3 utility knives, 1 chef's knife and 1 slicer. The profit is $30 on a basic set, $40 on a Regular set, and $60 on a Deluxe set. The factory has on hand 800 utility knives, 400 chef's knives, and 200 slicers. assuming that all sets will be sold, how many of each type should be made up in order to maximize profit? what is the maximum profit?
Formulation of the LPP
For maximum profit, let the number of sets to be sold be x of the Basic type, y of the Regular type and z of the Deluxe type.
Maximize P = 30x + 40y + 60z subject to
2x + 2y + 3z 800 (Utility knives constraint)
x + y + z 400 (Chefs knives constraint)
y + z 200 (Slicers constraint)
x, y, z 0
Tableau #1
x
y
z
s1
s2
s3
p
2
2
3
1
0
0
0
800
1
1
1
0
1
0
0
400
0
1
1
0
0
1
0
200
-30
-40
-60
0
0
0
1
0
Tableau #2
x
y
z
s1
s2
s3
p
2
-1
0
1
0
-3
0
200
1
0
0
0
1
-1
0
200
0
1
1
0
0
1
0
200
-30
20
0
0
0
60
1
12000
Tableau #3
x
y
z
s1
s2
s3
p
1
-0.5
0
0.5
0
-1.5
0
100
0
0.5
0
-0.5
1
0.5
0
100
0
1
1
0
0
1
0
200
0
5
0
15
0
15
1
15000
The optimum solution is x = 100 (Basic Type), y = 0 (Regular Type), z = 200 (Deluxe Type) and profit, P = $15000.
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