Chapter 12: Linear Programming

Question 1

When is linear programming used?

Answer 1

When there is more that one scarce resource.

Question 2

How do we solve linear programming problems?

Answer 2

Define the variables
Determine and state the objective function
State the constraints
Plot the constraints on a graph
Find the optimal solution

Question 3

What is slack?

Answer 3

The amount of each resource which will be unused if a specific linear programming solution is implemented.

Question 4

What is surplus?

Answer 4

Utilisation of a resource over and above a minimum.

Question 5

What is a shadow price?

Answer 5

Increase in contribution that could be created by having one more unit of the limiting factor at the original cost.

Question 6

How do you calculate shadow price?

Answer 6

Calculating the increase in value (usually extra contribution) which would be created by having available one additional unit of a limiting resource at its original cost.

1. Take equation of straight lines that intersect at the optimal point. Add one unit to the constraint concerned, while leaving the other critical constraint unchanged
2. Use simultaneous equations to derive a new optimal solution
3. Calculate revised optimal contribution and compare to original contribution calculated. The increase is the shadow price

Question 7

What are the limitations of linear programming?

Answer 7

It assumes that all relationships are linear
Suitable when one clearly defined objective function
Can become too complex to solve manually
It assumes that all variables are completely divisible
Single value estimates are used
It assumes that the situation remain static in all other respects