Linear programming

Question 1

What is linear programming?

Answer 1

This is a mathematical model used to determine the optimal use of more than one scarce resource. This provides an optimal product production mix for the products in the organisations portfolio.

Question 2

Why is linear programming necessary?

Answer 2

When there is more than one scarce resource, then limiting factor analysis will not be sufficient

Question 3

Five steps to solving linear programming problems

Answer 3

1. Define the variables.
2. Determine the objective function ( this will normally be to maximise contribution)
3. State the constraints. ( each scarce resource will be expressed as an equation)
4. The constraints on graph.
5. Find the optimal solution.( this will be in the feasible region.)

Question 4

What is an iso contribution line?

Answer 4

An iso contribution is a profit line that shows all combinations of X and why that provide the same total for the objective function

The iso contribution line can be used to identify the solution to the linear programming problem. Bye using a ruler to push this line away from the origin within the feasible region to see the possible outcome.

Question 5

What is slack and surpluses?

Answer 5

Slack
Is the amount of each resource which will be unused if a specific linear programming solution is implemented?.
There will be no slack for critical constraints as they will be fully utilised

Surplus
The utilisation of a resource over and above the minimum . For example, minimum was six, but we made eight.

Question 6

What are shadow prices?

Answer 6

The shadow price is the increase in contribution that could be created by having one more unit of the limiting factor.

It is the opportunity cost of not having the unit available.

It represents the maximum premium that the firm should be willing to pay for one extra unit of each constraint .

For non-critical constraints, the shadow price will be zero a slack already exists.

Question 7

How to calculate shadow prices

Answer 7

1. Take the equations of the straight lines that intersect at the optimal point and add one unit to the constraint concerned whilst leaving the other unchanged
2. Use simultaneous equations to find a new optimal solution.
3. calculate the revised optimal contribution and compare to the original contribution calculated

Question 8

What are the limitations of linear programming?

Answer 8

• it assumes all relationships are linear
• only suitable when there is a single clearly defined objective function
• To complex to solve manually
• Assumes all variables are completely divisible
• Single value estimates are used
• Assumes situation remains static in all other respects