The Good to Go Suitcase company makes three kinds of suitcases: (1) Standard, De
ID: 3050605 • Letter: T
Question
The Good to Go Suitcase company makes three kinds of suitcases: (1) Standard, Deluxe and Luxury styles. Each suitcase goes through four stages: cutting and coloring, assembly, finishing, and quality and packaging. The total numbers of hours available in each of these departments is 630,600, 708 and 135 respectively. The company wants to keep production of Luxury to a maximum of 40 % of total production.
Financial data ($ per unit) on this operation as well as production (hours) and demand data (unit)
are, provided in the table below.
Suitcase
Standard
Deluxe
Luxury
Selling price/unit
$36.05
$39.5
$43.3
Material Cost/unit
6.25
7.5
8.5
Labour cost/unit
19.8
23.00
25.3
Profit/ Unit
10.00
9.00
9.5
Production Data
Available hours
Cutting and coloring hrs/unit
.70
1.0
1.0
630
Assembly hours/unit
0.50
0.83
0.67
600
Finishing hours/unit
1.0
0.67
0.90
708
Quality & packaging
0.10
0.25
0.40
135
Market Data
Maximum Demand
600
300
150
Minimum To Make
400
150
50
Variables are the number (#) produced. Let X1 = # of Standard, X2 = # of Deluxe , X3 = number of Luxury produced.
Maximise
10X1 + 9X2 + 9.50X3 Profit function
Subject to
0.70X1 + 1.0X2 + 1.0X3 630 (1) Use of cutting and coloring hours
0.50X1 + 0.83X2 + 0.67X3 600 (2) Use of Assembly hours
1.0XI +0.67X2+0.90X3708 (3) Use of Finishing hours
0.10x1+0.25X2+0.40X3135 (4) Quality and packaging
X1 600, X2 300, X3150 (5-6) Max to make based on demand
X1 500, X2250, X350 (7-9) Min to make based on demand
X3 0.40 (X 1 + X2 + X3) (10) Max based on ratio for luxury
Microsoft Excel 12.0 Answer Report
Target Cell (Max)
Cell
Name
Original Value
Final Value
$E$9
profit
-
7,607.02
Adjustable Cells
Cell
Name
Original Value
Final Value
$B$5
Number of units Standard
-
516.76
$C$5
Number of units Deluxe
-
218.27
$D$5
Number of units Luxury
-
50.00
Constraints
Cell
Name
Cell Value
Formula
Status
Slack
$E$11
Cutting and coloring hrs/unit
630.00
$E$11<=$G$11
Binding
-
$E$12
Assembly hours/unit
473.04
$E$12<=$G$12
Not Binding
126.96
$E$13
Finishing hours/unit
708.00
$E$13<=$G$13
Binding
-
$E$14
Quality &packaging
126.24
$E$14<=$G$14
Not Binding
8.76
$E$15
Max luxury ratio
(264.01)
$E$15<=$G$15
Not Binding
264.01
$E$16
Maximum standard
516.76
$E$16<=$G$16
Not Binding
83.24
$E$17
Max for deluxe
218.27
$E$17<=$G$17
Not Binding
81.73
$E$18
Max for luxury
50.00
$E$18<=$G$18
Not Binding
100.00
$E$19
Min for Standard
516.76
$E$19>=$G$19
Not Binding
????
$E$20
Min for Deluxe
218.27
$E$20>=$G$20
Not Binding
68.27
$E$21
Min for Luxury
50.00
$E$21>=$G$21
Binding
-
-
Adjustable Cells
Final
Reduced
Objective
Allowable
Allowable
Cell
Name
Value
Cost
Coefficient
Increase
Decrease
$B$5
Number of units Standard
516.76
0
10
3.43
2.55
$C$5
Number of units Deluxe
218.27
0
9
5.29
1.58
$D$5
Number of units Luxury
50
0
9.5
1.10
1E+30
Constraints
Final
Shadow
Constraint
Allowable
Allowable
Cell
Name
Value
Price
R.H. Side
Increase
Decrease
$E$11
Cutting and coloring hrs/unit
630.00
4.331
630
25.410
36.250
$E$12
Assembly hours/unit
473.04
0
600
1E+30
126.958
$E$13
Finishing hours/unit
708.00
6.968
708
44.2
62.000
$E$14
Quality &packaging
126.24
0
135
1E+30
8.757
$E$15
Max luxury ratio
-264.01
0
0
1E+30
264.011
$E$16
Maximum standard
516.76
0
600
1E+30
83.239
$E$17
Max for deluxe
218.27
0
300
1E+30
81.733
$E$18
Max for luxury
50.00
0
150
1E+30
100.000
$E$19
Min for Standard
516.76
0
400
116.761
1E+30
$E$20
Min for Deluxe
218.27
0
150
68.267
1E+30
$E$21
Min for Luxury
50
-1.10
50
47.988
50
QUESTIONS
a) What is the optimal solution in words?
b) 20 hours of labour for cutting and colouring were lost. Evaluate the effect.
Suitcase
Standard
Deluxe
Luxury
Selling price/unit
$36.05
$39.5
$43.3
Material Cost/unit
6.25
7.5
8.5
Labour cost/unit
19.8
23.00
25.3
Profit/ Unit
10.00
9.00
9.5
Production Data
Available hours
Cutting and coloring hrs/unit
.70
1.0
1.0
630
Assembly hours/unit
0.50
0.83
0.67
600
Finishing hours/unit
1.0
0.67
0.90
708
Quality & packaging
0.10
0.25
0.40
135
Market Data
Maximum Demand
600
300
150
Minimum To Make
400
150
50
Explanation / Answer
a) The optimal solution in words.
The optimal solution is Seven thousand six hundred, seven and two hundredths. This is the final value of the profit function from the answer report.
b) If 20 hours of labour for cutting and colouring were lost.
The shadow price of cutting and colouring constraint is 4.331. This shadow price indicates that if the cutting and coloring hours is increased by one unit the profit will increase by 4.331. If the cutting and coloring hours is decreased by one unit the profit will decrease by 4.331.
So if 20 hours of labour for cutting and colouring were lost, the profit will decrease by 86.62.
The new optimal solution will become seven thousand, twenty and four tenths (or 7520.40).
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