Linear Programming

Question 1

What is Linear Programming?

Answer 1

Technique of allocating resources to achieve the best results/objectives.
Different constraints and profit margins per business.
Use when 1 or more limiting factor.

Question 2

What are the Methods to Solve a Linear Programming Problem?

Answer 2

• Graphical approach, draw limiting resource equations, find edge of feasible region. Can use Excel.
  2. Simplex algorithm.

Question 3

What Are Major Assumptions About Linear Programming?

Answer 3

Additivity
Divisibility
Constant unit VC
FC stays the same regardless
Estimates of sales D are certain

Question 4

What is Additivity?

Answer 4

Unit A requires 3hrs labour & 15kg material.
Unit B requires 2hrs labour & 5kg material.
A+B = 5hrs labour & 20kg material.

Question 5

What is Divisibility?

Answer 5

Total resources required are directly proportional to volume output.
12 units of C required 24hrs labour & 36kg material.
One unit of C requires 2hrs labour and 3kg materials.

Question 6

Contribution =

Answer 6

Sale Price – Variable Costs

Question 7

What is the Graphical Approach

Answer 7

Cannot be used if there is more than 2 variables.
No. of constraints is insignificant.

Question 8

What is the Iso-Profit Line within the Graphical Approach?

Answer 8

Shows Optimum Solution. Where it leaves feasible region, sub quantities into equation to find maximum values.

Question 9

What is the Optimal Solution?

Answer 9

Used to find constraints, costs, and prices are known a at a fixed quantity.
Can also be used to test.
Also used to test how solution changes if quantity of scarce resource changes.

Question 10

How is a Constraint Binding?

Answer 10

If changing it alters the optimal solution.

Question 11

What is Sensitivity Analysis?

Answer 11

Tests how optimal solution changes if there was more/less scarce resources.
Worth while changing Q?

Question 12

What are Shadow Prices?

Answer 12

Change in contribution created by changing number of units of a limiting resource.
Determines max worth paying for additional scarce resources.
Important for cost control & transfer pricing.

Question 13

Assumptions & Limitations of Linear Programming:

Answer 13

• FC remain the same
• Unit VC is constant
• Estimates = certainty
• Units of output are divisible
• In practice, difficult to determine which resources are likely to be in short supply, how much will be available, and whether all possible uses have been identified

Question 14

When can Contribution be Worked out?

Answer 14

After item is sold.