the use of linear programming for the allocation of scarce resources
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LEARNING NOTE 11.1. The use of linear programming for the allocation of scarce resources. LN11.1 (1a). Linear programming. LN11.1 (1b). Example (cont.). LN11.1 (2). Materials constraint (8Y + 4Z 3,440 (When Y= 0, Z = 860; when Z= 0, Y = 430. LN11.1 (3). - PowerPoint PPT PresentationTRANSCRIPT
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
The use of linear programming for the allocation of scarce resources
LEARNING NOTE 11.1
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Linear programming
LN11.1 (1a)
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Example (cont.)
LN11.1 (1b)
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Materials constraint (8Y + 4Z 3,440 (When Y= 0, Z = 860;when Z= 0, Y = 430
LN11.1 (2)
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Labour constraint 6Y + 8Z 2,880 (when Z = 0, Y = 480;when Y = 0, Z = 360)
LN11.1 (3)
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Machine capacity constraint 4Y + 6Z 2,760 (when Z = 0, Y = 690; when y = 0, Z = 460)
LN11.1 (4)
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Sales limitation Y 420
LN11.1 (5)
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Optimum solution
Feasible production combination = Area ABCDE
LN11.1 (6)
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Optimum solution
1. The optimum output can be determined by solving the simultaneous equations that intersect at point C:
8Y + 4Z = 3 440
6Y + 8Z = 2 880
so that Y = 400 and Z = 60
LN11.1 (7a)
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Optimum solution
2. The materials and labour constraints are binding and therefore have opportunity costs. The marginal contribution from obtaining one extra unit of materials can be calculated by solving the following equations:
8Y + 4Z = 3 441 (revised materials constraint)
6Y + 8Z = 2 880 (unchanged labour constraint)
Y = 400.2 units, Z = 59.85 units
Therefore the planned output of Y would be increased by 0.2 units and Z reduced by 0.15 units and contribution will increase by £0.40 (the opportunity cost).
LN11.1 (7b)
Cost and Management Accounting: An Introduction, 7 th editionColin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Optimum solution
3. The marginal contribution from obtaining one extra labour hour can be found in a similar way:
8Y + 4Z = 3 400 (unchanged materials constraint)
6Y + 8Z = 2 881 (revised labour constraint)
Y = 399.9 and Z = 60.2
Marginal contribution = £1.80
LN11.1 (7c)