Seminar exercises
Product-mix decisions
Corporation system-matrix
1.) Resource-product matrix
Describes the connections between the company’s
resources and products as linear and deterministic
relations via coefficients of resource utilization and resource
capacities.
2.) Environmental matrix (or market-matrix):
Describes the minimum that we must, and maximum
that we can sell on the market from each product. It
also desribes the conditions.
Resource-product matrix
Product
types
P1
Pi
Pn
Resources
Capacities
R1
R2
a11
a21
a1i
a2i
a1n
a2n
b1
b2
Ri
a i1
aii
a
in
bi
Rm
am1
am i
amn
bm
Resource
utilization
coefficients
Rnvironmental matrix
P1
MIN
MAX
Price (p)
Contribution
margin per
unit (CM)
…
Pi
…
Pn
Contribution margin



(Unit Price) – (Variable Costs Per Unit) =
(Contribution Margin Per Unit)
(Contribution Margin Per Unit) x (Units Sold) =
(Product’s Contribution to Corporate Profit)
(Contributions to Profit From All Products) –
(Firm’s Fix Costs) = (Total Profit)
Resource-Product Relation types
P1
P6
P7
R5
a56
a57
R6
a66
a67
R1
P2
P3
P4
P5
a43
a44
a45
a11
R2
a22
R3
a32
R4
Non-convertible relations
Partially convertible relations
Product-mix in a pottery –
corporate system matrix
Jug
Plate
Capacity
Clay (kg/pcs)
1,0
0,5
50 kg/week
100 HUF/kg
Weel time
(hrs/pcs)
Paint (kg/pcs)
0,5
1,0
50 hrs/week
800 HUF/hr
0
0,1
10 kg/week
100 HUF/kg
Minimum
(pcs/week)
10
10
Maximum
(pcs/week)
100
100
Price (HUF/pcs)
700
1060
Contribution
margin (HUF/pcs)
200
200
e1:
1*P1+0,5*P2 < 50
e2:
0,5*P1+1*P2 < 50
e3:
0,1*P2 < 10
p1 , p2 :
10 < P1 < 100
p3 , p4 :
10 < P2 < 100
ofF:
200 P1+200P2=MAX
Objective function

refers to choosing the best element from some
set of available alternatives.
X*P1 + Y*P2 = max
weights
(depends on what we want to maximize:
price, contribution margin)
variables
(amount of produced goods)
Solution with linear programming
P1
33 jugs and 33 plaits a
per week
e1
100
ofF
e3
e1:
1*P1+0,5*P2 < 50
e2:
0,5*P1+1*P2 < 50
e3:
0,1*P2 < 10
p1,p2:
10 < P1 < 100
p3 , p4 :
10 < P2 < 100
ofF:
200 P1+200P2=MAX
33,3
e2
100
33,3
Contribution margin: 13
200 HUF / week
P2
What is the product-mix, that maximizes the
revenues and the contribution to profit!
P1
R1
P2
P3
P4
P5
P6
4
2 000
2
R2
b (hrs/y)
1
3 000
1
R3
1 000
R4
2
3
6 000
R5
2
2
5 000
MIN (pcs/y)
100
200
200
200
50
100
MAX (pcs/y)
400
1100
1 000
500
1 500
2000
p (HUF/pcs)
200
270
200
30
50
150
f (HUF/pcs)
100
110
50
-10
30
20
Solution

P1:
Resource constraint 2000/4 = 500
> market constraint 400

P2-P3: Which one is the better product?
Rev. max.:
270/2 < 200/1
thus P3
P3=(3000-200*2)/1=2600>1000
P2=200+1600/2=1000<1100
Contr. max.: 110/2 > 50/1
thus P2
P2=(3000-200*1)/2=1400>1100
P3=200+600/1=800<1000

P4: does it worth?
Revenue max.: 1000/1 > 500
Contribution max.: 200

P5-P6: linear programming
e1:
e2:
p1, p2:
p3, p4:
cfÁ:
cfF:
2*P5 + 3*P6 ≤ 6000
2*P5 + 2*P6 ≤ 5000
50 ≤ P5 ≤ 1500
100 ≤ P6 ≤ 2000
50*P5 + 150*P6 = max
30*P5 + 20*P6 = max
P5
e1
3000
Profit max: P5=1500, P6=1000
TR max: P5=50, P6=1966
e2
2500
cfF
cfÁ
2000
2500
P6