3. Concepts to be covered in
lecture
1) Unconstrained optimisation.
2) Constrained optimisation.
3) Linear programming.
Primal problem.
Shadow prices.
Profit maximisation.
Cost minimisation.
4.
5.
6.
7.
8.
9.
10. Corner Point Combination Cost
a 2.5A +0B £ 1250
b 5/3A + 2/3B £ 1233
c 0A + 4B £ 2400
The lowest cost is £ 1233 and it requires 5/3 cases of
type A and 2/3 cases of type B per production run to be
produced.
Contribution per one unit of constraint (shadow prices)
10 VHR + 20 VM + 10VC (HR = labour component, M =
material, C = production capital
and V = shadow price)
and 4VHR + 10VM + 5VC = 500
5VHR + 5VM + 4VC = 600
The slack variable is production capital
4 VHR + 10VM = 500
and 5 VHR + 5VM = 600
Simultaneous solving for two unknowns result in:
VHR = 116 2/3
& VM = 3 1/3
Every one additional HR – input will add £ 116.66 to
total cost and one additional unit of material will add
£ 3.33 to total cost.