dmm1
TRANSCRIPT
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9/7/2011
SUBMITTED TO:
Dr. Hitesh Arora
Submitted by:
Samridhi Madaan
FMG20C
ROLL NO.- 201142
R.L.
FURNITURESDMM:CASESTUDY
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A furniture Company produces three types of furniture- End Tables, sofas and Chairs. These products
are processed in five departments- Saw Lumber, Cut Fabric, Sand, Stain and Assemble. Each chair
and tables are produced from raw lumber only, and the sofas require lumber and fabric. Glue and
thread are plentiful and represent a relatively insignificant cost that is included in operating expense.
The specific requirements for each product are as follows:
RESOURCE ACTIVITY(
QUANTITY AVAILABLE
PER MONTH)
REQUIRED PER END
TABLE
REQUIRED PER SOFA REQUIRED PER CHAIR
Lumber( 4350 broad
feet)
10 board feet @ Rs.
10/foot= Rs. 100/table
7.5 board feet @ Rs.
10/foot= Rs. 75
4 board feet @ Rs.
10/foot = Rs. 40
Fabric(2500 yards) None 10 yards @ Rs. 17.50/
yard= Rs. 175
None
Saw lumber (280
hours)
30 minutes 24 minutes 30 minutes
Cut fabric (140 hours) None 24 minutes None
Sand (280 hours) 30 minutes 6 minutes 30 minutesStain (140 hours) 24 minutes 12 minutes 24 minutes
Assemble (700 hours) 60 minutes 90 minutes 30 minutes
The companys direct labour expenses are Rs. 75,000 per month for the 1,540 hours of labour, at Rs.
48.70 per hour. Based on current demand, the firm can sell 300 end tables, 180 sofas and 400 chairs
per month. Sales prices are Rs. 400 for end tables, Rs. 750 for sofas and Rs. 240 for chairs. Assume
that labour cost is fixed and the firm does not plan to hire or fire any employees over the next
month.
a. What is the most limiting resource to the furniture company?b. Determine the product mix needed to maximize the profit at the furniture company. What is
the optimal number of end tables, sofas and chairs to produce each month?
c. What is the impact of shadow prices?
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Solution:
Defining X1 as the number of end tables,
X2 as the number of sofas,
and X3 as the number of chairs to produce each month.
Profit is calculated as the revenue for each item minus the cost of materials (lumber and fabric)
minus the cost of labour.
Since each labour is fixed, we subtract this (Rs. 75,000) out as a total sum.
Mathematically we have,
Materials used Cost of End Tables Cost Of Sofas Cost of Chairs
Lumber 100 75 40
Fabric 0 175 0
Total Cost 100 250 40
Sales 400 750 240
Profit 300 500 200
Profit is calculated as follows:
Profit = 400X1 + 750X2 +240X3 75,000
We have to maximise the profit (Z).
Constraints are the following:
Lumber availability
10X1 + 7.5X2 + 4X3
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Assemble availability
1X1 + 1.5X2 + 0.5X3
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Now we will solve the table in Excel using data solver:
Step 1: here we will get the initial values. Wherein we get the number of sofas to be produced which
is 180 and the profit is Rs. 15,000.
End Tables Sofas chairs Total Limit
Changing cells 0 180 0
Profit 300 500 200 15000
Lumber 10 7.5 4 1350 4350
Fabric 0 10 0 1800 2500
Saw 0.5 0.4 0.5 72 280
cut table 0 0.4 0 72 140
Sand 0.5 0.1 0.5 18 280
Strain 0.4 0.2 0.4 36 140
Assemble 1 1.5 0.5 270 700Table Demand 1 0 300
Sofa Demand 1 180 180
Chair Demand 1 0 400
Step 2: Again by using solver we get the final values where our profit is Rs. 93,000.
End Tables Sofas Chairs Total Limit
Changing cells 260 180 0
Profit 300 500 200 93000
Lumber 10 7.5 4 3950 4350
Fabric 0 10 0 1800 2500
Saw 0.5 0.4 0.5 202 280
cut table 0 0.4 0 72 140
Sand 0.5 0.1 0.5 148 280
Strain 0.4 0.2 0.4 140 140
Assemble 1 1.5 0.5 530 700
Table Demand 1 260 300
Sofa Demand 1 180 180Chair Demand 1 0 400
Final Result: After solving the problem we get final values as follows:
Maximum profit which can be earned is Rs. 93,000.
Cell Name Original Value Final Value
$E$5 Profit Total 93000 93000
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End table 260 units
Sofas 180 units
And we are not producing Chairs, i.e. number of chairs is zero.
Cell Name Original Value Final Value
$B$4 Changing cells End Tables 260 260
$C$4 Changing cells Sofas 180 180
$D$4 Changing cells chairs 0 0
Constraints:
Cell Name Cell Value Formula Status Slack
$E$7 Lumber Total 3950 $E$7
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Revenue for each table can range from Rs1000 (Rs. 300+ Rs. 700) to Rs. 200 (Rs. 300- Rs.100).
Here, the value for 1E+30 is a very large number, especially infinity.
Constraints:
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$F$7 Lumber Total 3950 0 4350 1E+30 400
$F$8 Fabric Total 1800 0 2500 1E+30 700
$F$9 Saw Total 202 0 280 1E+30 78
$F$10 cut table Total 72 0 140 1E+30 68
$F$11 Sand Total 148 0 280 1E+30 132
$F$12 Strain Total 140 749.9999992 140 16 104
$F$13 Assemble Total 530 0 700 1E+30 170
$F$14 Table Demand
Total
260 0 300 1E+30 40
$F$15 Sofa Demand
Total
180 350.0000006 180 70 80
$F$16 Chair Demand
Total
0 0 400 1E+30 400
Since the shadow prices of Lumber, Fabric, Saw and cut table is zero, there will be no impact of its
increase or decrease in the profit margin.
Also, the shadow price of strain is 749.99, it shows we can increase the profit by this amount just by
employing one additional unit of Strain. But the strain is fully utilised thus there will be no impact of
its increase in the profit.
The limiting resource in the production process is straining capacity; we can take benefit of the
allowable increase which is 16 hours to increase our profits as 1 hour increase in strain would
increase the profit by Rs. 749.99.
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REFRENCES:
1. For question, Operation Management For Competitive Advantage, Richards B. Chase and F.Jacob, Tata McGraw Hill
2. For excel formula,