Shelby Shelving - Current Production Schedule
Machine usage requirements (hours per unit)
Stamping Forming
Model S 0.30 0.25
Model LX 0.30 0.50
Monthly production
Model S 400
Model LX 1400
1900 $1,800
1400 $2,100
Assembly capacity Unit selling price
Available 800 800
Hours spent in departments Stamping Forming
Model S 120 100
Model LX 420 700
Totals 540 800
Percentages of time spent in departments Model S Model LX Stamping 22.2% 77.8% Forming 12.5% 87.5% Monthly overhead cost data
Stamping Forming Model S Assembly Model LX Assembly
Model S Variable $80 $120 $165 $0 $365
Model LX Variable $90 $170 $0 $185 $445
Total Fixed $125,000 $95,000 $80,000 $85,000 $385,000
Standard costs of the shelves (based on the current production levels)
Direct materials Direct labor: Stamping Forming Assembly Total direct labor Overhead allocation Stamping Forming Assembly Total overhead Total cost
Model S $1,000
Model LX $1,200
$35 $60 $80 $175
$35 $90 $85 $210
$149.44 $149.69 $365.00 $664.13 $1,839.13
$159.44 $229.38 $245.71 $634.53 $2,044.53
Microsoft Excel 12.0 Answer Report Worksheet: [Accounting 522_Shelby Shelving.xlsx]Shelby Linear Programming Report Created: 12/3/2014 12:45:49 AM
Target Cell (Max) Cell $C$37 Profit
Name
Original Value $62,000
Adjustable Cells Cell Name Original Value $C$11 Production per month Model S 400 $D$11 Production per month Model LX 1400
Final Value $268,250
$300,000 $250,000
Final Value 1900 650
$200,000 $150,000
Constraints Cell Name $C$18 Forming Hours used $C$17 Stamping Hours used $C$11 Production per month Model S $D$11 Production per month Model LX
$100,000
Cell Value 800 765 1900 650
Formula $C$18<=$E$18 $C$17<=$E$17 $C$11<=$C$13 $D$11<=$D$13
Status Slack Binding 0 Not Binding 35 Binding 0 Not Binding 750
$50,000 $0
Profit $300,000
$268,250
$250,000 $200,000 $150,000
Profit
$100,000 $62,000 $50,000 $0 Original Value
Final Value
Microsoft Excel 12.0 Sensitivity Report Worksheet: [Accounting 522_Shelby Shelving.xlsx]Shelby Linear Programming Report Created: 12/3/2014 12:45:49 AM
Adjustable Cells Final Reduced Objective Cell Name Value Cost Coefficient $C$11 Production per month Model S 1900 137.5 260 $D$11 Production per month Model LX 650 0 245
Allowable Allowable Increase Decrease 1E+30 137.5 275 245
Constraints Cell Name $C$18 Forming Hours used $C$17 Stamping Hours used
Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 800 490 800 58.33333334 325 765 0 800 1E+30 35
Microsoft Excel 12.0 Limits Report Worksheet: [Accounting 522_Shelby Shelving.xlsx]Limits Report 1 Report Created: 12/3/2014 12:45:49 AM
Cell $C$37 Profit
Target Name
Adjustable Cell Name $C$11 Production per month Model S $D$11 Production per month Model LX
Value $268,250
Value 1900 650
Lower Target Limit Result 0 -225750 0 109000
Upper Limit 1900 650
Target Result 268250 268250
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
B
C
D
E
F
G
H
I
J
K
L
M
N
O
Shelby Shelving - Linear Programming Profit Maximization Model Machine requirements (hours per unit)
Stamping Forming
Production per month Assembly capacity
Model S Model LX 0.30 0.30 0.25 0.50 Model S 1900 <= 1900
Model LX 650 <= 1400
Hours used 765 800
<= <=
Problem Statement: What is the optimal production mix for Shelby Shelving in order to maximize its profits?
Constraints on hourly usage Stamping Forming Profit analysis Unit selling price
$1,800
$2,100
Unit variable costs Labor Material Overhead Total Variable Cost
$175 $1,000 $365 $1,540
$210 $1,200 $445 $1,855
Contribution Margin Total Contribution
$260 $494,000
$245 $159,250
Total revenue Total variable cost Total Contribution Fixed overhead Profit
Available 800 800
Executive Summary: The profit maximization linear programming model suggests the optimal production mix is 1900 units of Model S and 650 units of Model LX. This will increase profit from $62,000 to $268,250, representing an increase of +433% over its current production schedule. If the Model S production increases from 400 units to its maximum capacity of 1900 units, the cost per unit will decrease from $1839 to $1661. Note: Given that the total number hours that can be used for Forming is 800 hours (which is used at full capacity), Shelby Shelving cannot produce any additional units of Model S or Model LX. If you try to increase it by 1 using the Developer Spinner button, the number of Forming hours used would EXCEED the given constraint of 800 hours
$4,785,000 $4,131,750 $653,250 $385,000 $268,250
Shelby Shelving Company LP Formulation
P
Shelby Shelving - Adjusted Production Schedule
Machine usage requirements (hours per unit)
Stamping Forming
Model S 0.30 0.25
Model LX 0.30 0.50
Monthly production
Model S 1900
Model LX 650
1900 $1,800
1400 $2,100
Assembly capacity Unit selling price
Available 800.00 800.00
Hours spent in departments Stamping Forming
Model S 570 475
Model LX 195 325
Totals 765 800
Percentages of time spent in departments Model S Model LX Stamping 74.5% 25.5% Forming 59.4% 40.6% Monthly overhead cost data
Stamping Forming Model S Assembly Model LX Assembly
Model S Variable $80 $120 $165 $0 $365
Model LX Variable $90 $170 $0 $185 $445
Total Fixed $125,000 $95,000 $80,000 $85,000 $385,000
Standard costs of the shelves (based on the current production levels)
Direct materials Direct labor: Stamping Forming Assembly Total direct labor Overhead allocation Stamping Forming Assembly Total overhead Total cost
Model S $1,000
Model LX $1,200
$35 $60 $80
$35 $90 $85
$175
$210
$129.02 $149.69 $207.11 $485.81 $1,660.81
$139.02 $229.38 $315.77 $684.16 $2,094.16
