This document provides an overview of concepts to be covered in an economics lecture, including: 1) Unconstrained and constrained optimization 2) Linear programming involving primal problems, shadow prices, and profit/cost minimization 3) An example of a corner point combination showing the lowest cost production requires 5/3 cases of good A and 2/3 cases of good B 4) Determining shadow prices by setting up and simultaneously solving equations involving labor, material, and production capital constraints

1. Economics
Optimisation (1)
(sphesihle MKHWANAZI)

2. References in textbook
Micro Management Economics
Section A Pages 2-13
Workbook section

3. Concepts to be covered in
lecture
 1) Unconstrained optimisation.
 2) Constrained optimisation.
 3) Linear programming.
 Primal problem.
 Shadow prices.
 Profit maximisation.
 Cost minimisation.

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.