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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,