1. Seminar exercises Product-mix decisions

2. 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.

3. Resource-product matrix1 i n R a 11 1i 1n b 2 21 2i 2n i1
i i
i n m m1
m i mn
Product types
Capacities
Resources
Resource utilization coefficients

4. Contribution margin per unit (CM)
Rnvironmental matrix P1 … Pi Pn
MIN
MAX
Price (p)
Contribution margin per unit (CM)

5. 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)

6. Resource-Product Relation types
Non-convertible relations R1
a11 R2
a22 R3
a32
Partially convertible relations R4
a43
a44
a45 R5
a56
a57 R6
a66
a67

7. Product-mix in a pottery – corporate system matrix
Jug
Plate
Capacity
50 kg/week
100 HUF/kg
50 hrs/week
800 HUF/hr
10 kg/week
Clay (kg/pcs)
1,0
0,5
Weel time (hrs/pcs)
0,5
1,0
Paint (kg/pcs)
0,1
Minimum (pcs/week) 10
Maximum (pcs/week)
100
Price (HUF/pcs)
700
1060
Contribution margin (HUF/pcs)
e1: 1*P1+0,5*P2 < 50
e2: 0,5*P1+1*P2 < 50
e3: ,1*P2 < 10
p1, p2: < P1 < 100
p3, p4: < P2 < 100
ofF: P1+200P2=MAX
200
200

8. variables (amount of produced goods)
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)

9. Solution with linear programming
33 jugs and 33 plaits a per week
Contribution margin: HUF / week P1 e1
100
ofF e3
e1: 1*P1+0,5*P2 < 50
e2: 0,5*P1+1*P2 < 50
e3: ,1*P2 < 10
p1,p2: < P1 < 100
p3, p4: < P2 < 100
ofF: P1+200P2=MAX
33,3 e2
100 P2
33,3

10. What is the product-mix, that maximizes the revenues and the contribution to profit!P1 P2 P3 P4 P5 P6
b (hrs/y) R1 4
2 000 R2 2 1
3 000 R3
1 000 R4 3
6 000 R5
5 000
MIN (pcs/y)
100
200 50
MAX (pcs/y)
400
1100
1 000
500
1 500
2000
p (HUF/pcs)
270 30
150
f (HUF/pcs)
110
-10 20

11. Solution P1: P2-P3: Which one is the better product?
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=( *2)/1=2600>1000
P2= /2=1000<1100
Contr. max.: 110/2 > 50/1 thus P2
P2=( *1)/2=1400>1100
P3= /1=800<1000

12. P5-P6: linear programming
P4: does it worth?
Revenue max.: 1000/1 > 500
Contribution max.: 200
P5-P6: linear programming
e1: 2*P5 + 3*P6 ≤ 6000
e2: 2*P5 + 2*P6 ≤ 5000
p1, p2: 50 ≤ P5 ≤ 1500
p3, p4: 100 ≤ P6 ≤ 2000
cfÁ: 50*P *P6 = max
cfF: 30*P5 + 20*P6 = max

13. P5 e1
Profit max: P5=1500, P6=1000
TR max: P5=50, P6=1966
3000 e2
2500
cfF
cfÁ
2000
2500 P6