Linear Pogramming

Question 1

What is linear programming?

Answer 1

If there is an optimum solution required in a situation where a company produces two products and there are limited resources the following can be used:
Graphical method
Simultaneous equations method
Linear programming is a powerful mathematical technique that can be applied to the problem of rationing limited facilities and resources among many alternative uses in such a way that the optimum benefits can be derived from their utilization” (Drury, 2012, p. 656)

A widely used mathematical programming technique
Used in a situation where there are two or more resource constraints
A method which balances many factors to obtain a predetermined objective i.e maximise contribution or minimise cost
Practical uses: planning production to maximise profit, mixing ingredients to minimise cost, selecting a portfolio of investments to maximise worth, scheduling jobs to minimise time

Question 2

What is the method of linear programming graphical and method?

Answer 2

1.Define the variables

2. State the objective function
   The objective function is a quantified statement of the aim of a resource allocation decision – maximise contribution or minimise costs
3. State the constraints(limiting factors)
   A constraint is an activity, resource or policy that limits the ability to achieve objectives

4.Draw a graph and find the feasible region

5. Find the optimum solution within the feasible region
   Draw an iso-contribution (profit) line where all points represent an equal contribution
   The outer most point in the feasible region will be the optimal solution

Question 3

What is the method for simultaneous equation?

Answer 3

1.Define the variables

2. State the objective function
   The objective function is a quantified statement of the aim of a resource allocation decision – maximise contribution or minimise costs
3. State the constraints(limiting factors)
   A constraint is an activity, resource or policy that limits the ability to achieve objectives
4. Solve using simultaneous equations
   Each equation represents a straight line on a graph and solving using simultaneous equations is the same as identifying the point at which 2 lines cross
   With the 2 equations at each of the points:
   Multiply both sides by the same amount
   Add or subtract one equation from the other

Question 4

What are the uses of linear programming?

Answer 4

Calculation of relevant costs
Selling different products
Maximum payment for additional scarce resources
Control
Managing constraints
Capital budgeting
Sensitivity analysis

Question 5

What is slack?

Answer 5

The amount by which a resource is under utilised

Question 6

What is shadow price?

Answer 6

An increase in value which would be created by having one additional unit of a limiting resource at its original cost

Question 7

What are the limitations of linear programming?

Answer 7

Linear relationships
Suitable only when one clearly defined objective function
Can become too complex to solve manually
Variables are completely divisible
Single value estimates are used
Situation remains static in all other respects