Homework SourseHow many Basic Sets should be made up Enter your answer A co
How many Basic Sets should be made up?
Enter your answer:
| A company sells sets of kitchen knives. A Basic Set consists of 4 utility knives and 1 chef\'s knife. A Regular Set consists of 2 utility knives, 1 chef\'s knife, and 1 slicer. A Deluxe Set consists of 4 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 900 utility knives, 300 chef\'s knives, and 100 slicers. If all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum profit? |
Solution
Solution:
Let x be the total number of basic set of knives
Let y be the total number of regular set of knives
Let z be the total number of Deluxe set of knives
As per given condtion
set of all utility kinves
4x +2y +4z <=900
for chef\'s knives
1x + y +z <= 300
for slicer
0x + y + z <=100
Now we have obejctive function : p = 30x + 40y + 60z which has to be maximized
using simplex method
Maximize p = 30x +40y+60z subject to
4x +2y +4z <=900
x + y +z <= 300
y+z <= 100
Tableau #1
x y z s1 s2 s3 p
4 2 4 1 0 0 0 900
1 1 1 0 1 0 0 300
0 1 1 0 0 1 0 100
-30 -40 -60 0 0 0 1 0
Tableau #2
x y z s1 s2 s3 p
4 -2 0 1 0 -4 0 500
1 0 0 0 1 -1 0 200
0 1 1 0 0 1 0 100
-30 20 0 0 0 60 1 6000
Tableau #3
x y z s1 s2 s3 p
1 -0.5 0 0.25 0 -1 0 130
0 0.5 0 -0.25 1 0 0 75
0 1 1 0 0 1 0 100
0 5 0 7.5 0 30 1 9800
therefore
Optimal Solution: p = 9800;
x = 130,
y = 0,
z = 100
therefore
Company has to produce x = 130 unit utility knives and y = 0 unit of chef\'s and z = 100 unit of slicer
and maximum profit = $9800
