A company sells sets of kitchen knives. A Basic Set consists of 44 utility knive
ID: 3033375 • Letter: A
Question
A company sells sets of kitchen knives. A Basic Set consists of 44 utility knives and 1 chef's knife. A Regular Set consists of 22 utility knives, 1 chef's knife, and 1 slicer. A Deluxe Set consists of 33 utility knives, 1 chef's knife, and 1 slicer. The profit is $30 on a Basic Set, $40 on a Regular Set, and $80 on a Deluxe Set. The factory has on hand 1200 utility knives, 600 chef's knives, and 300 slicers. If all sets will be sold, how many of each type should be made up in order to maximizeprofit? What is the maximum profit?
Explanation / Answer
Let x nos. of basic set , y nos. of regular set and z nos of deluxe sets are sold
Profit , P = 30x+ 40y + 80z
Utility Knives :44x + 22y +33z <= 1200
chefs knives : x+y +z <= 600
slicer : y +z <=300
Solve the inequalties : use simplex method
Tableau #1
x y z s1 s2 s3 s4 s5 s6 p
44 22 33 1 0 0 0 0 0 0 1200
1 1 1 0 1 0 0 0 0 0 600
0 1 1 0 0 1 0 0 0 0 300
1 0 0 0 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 0 -1 0 0
-30 -40 -80 0 0 0 0 0 0 1 0
Tableau #2
x y z s1 s2 s3 s4 s5 s6 p
44 22 33 1 0 0 0 0 0 0 1200
1 1 1 0 1 0 0 0 0 0 600
0 1 1 0 0 1 0 0 0 0 300
-1 0 0 0 0 0 1 0 0 0 0
0 1 0 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 0 -1 0 0
-30 -40 -80 0 0 0 0 0 0 1 0
Tableau #3
x y z s1 s2 s3 s4 s5 s6 p
44 22 33 1 0 0 0 0 0 0 1200
1 1 1 0 1 0 0 0 0 0 600
0 1 1 0 0 1 0 0 0 0 300
-1 0 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 0 -1 0 0
-30 -40 -80 0 0 0 0 0 0 1 0
Tableau #4
x y z s1 s2 s3 s4 s5 s6 p
44 22 33 1 0 0 0 0 0 0 1200
1 1 1 0 1 0 0 0 0 0 600
0 1 1 0 0 1 0 0 0 0 300
-1 0 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 0 1 0 0
-30 -40 -80 0 0 0 0 0 0 1 0
Tableau #5
x y z s1 s2 s3 s4 s5 s6 p
1.33333 0.666667 1 0.030303 0 0 0 0 0 0 36.3636
-0.333333 0.333333 0 -0.030303 1 0 0 0 0 0 563.636
-1.33333 0.333333 0 -0.030303 0 1 0 0 0 0 263.636
-1 0 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 0 1 0 0 0
1.33333 0.666667 0 0.030303 0 0 0 0 1 0 36.3636
76.6667 13.3333 0 2.42424 0 0 0 0 0 1 2909.09
Optimum solution for maximium profit : x=0 ; y =0; z = 36.36 = 36
Profit = 2909.09 = $2909
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