Seminar exercises The Productmix Problem Agnes Kotsis Corporate
Seminar exercises The Product-mix Problem Agnes Kotsis
Corporate 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 Resources Capacities Resource utilization coefficients
Environmental matrix T 1 MIN MAX Price (p) Contribution margin per unit (f) … Ti … Tn
Contribution margin Unit Price - Variable Costs Per Unit = Contribution Margin Per Unit n Contribution Margin Per Unit x Units Sold = Product’s Contribution to Profit n Contributions to Profit From All Products – Firm’s Fixed Costs = Total Firm Profit n
Resource-Product Relation types T 1 T 6 T 7 E 5 a 56 a 57 E 6 a 67 E 1 T 2 T 3 T 4 T 5 a 43 a 44 a 45 a 11 E 2 a 22 E 3 a 32 E 4 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 Price (HUF/pcs) 700 200 1060 200 Contribution margin (HUF/pcs) e 1 : 1*T 1+0, 5*T 2 < 50 e 2 : 0, 5*T 1+1*T 2 < 50 e 3 : 0, 1*T 2 < 10 p 1 , p 2 : 10 < T 1 < 100 p 3 , p 4 : 10 < T 2 < 100 of. F: 200 T 1+200 T 2=MAX
Objective function n refers to choosing the best element from some set of available alternatives. X*T 1 + Y*T 2 = max weights (depends on what we want to maximize: price, contribution margin) variables (amount of produced goods)
Solution with linear programming T 1 33 jugs and 33 plaits a per week e 1 100 of. F e 3 e 1 : 1*T 1+0, 5*T 2 < 50 e 2 : 0, 5*T 1+1*T 2 < 50 e 3 : 0, 1*T 2 < 10 p 1, p 2: 10 < T 1 < 100 p 3 , p 4 : 10 < T 2 < 100 of. F: 200 T 1+200 T 2=MAX 33, 3 e 2 100 33, 3 Contribution margin: 13 200 HUF / week T 2
What is the product-mix, that maximizes the revenues and the contribution to profit! T 1 E 1 T 2 T 3 T 4 T 5 T 6 4 2 000 2 E 2 b (hrs/y) 1 3 000 1 E 3 1 000 2 2 E 4 E 5 3 2 6 000 5 000 MIN (pcs/y) 100 200 200 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 n T 1: Resource constraint 2000/4 = 500 > market constraint 400 n T 2 -T 3: Which one is the better product? Rev. max. : 270/2 < 200/1 thus T 3=(3000 -200*2)/1=2600>1000 T 2=200+1600/2=1000<1100 Contr. max. : 110/2 > 50/1 thus T 2=(3000 -200*1)/2=1400>1100 T 3=200+600/1=800<1000
n T 4: does it worth? Revenue max. : 1000/1 > 500 Contribution max. : 200 n T 5 -T 6: linear programming e 1: e 2: p 1, p 2: p 3, p 4: cfÁ: cf. F: 2*T 5 + 3*T 6 ≤ 6000 2*T 5 + 2*T 6 ≤ 5000 50 ≤ T 5 ≤ 1500 100 ≤ T 6 ≤ 2000 50*T 5 + 150*T 6 = max 30*T 5 + 20*T 6 = max
T 5 e 1 3000 Contr. max: T 5=1500, T 6=1000 Rev. max: T 5=50, T 6=1966 e 2 2500 cf. F cfÁ 2000 2500 T 6
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