Linear Programming

Question 1

How can management science be used for manufacturing?

Answer 1

Calculating how to allocate limited resources to give maximum profit

Question 2

How can management science be used for transportation?

Answer 2

Minimising the transportation costs for e.g. delivery

Question 3

How can management science be used for facilities planning?

Answer 3

Where things can be located so they’re in the best position for their use, e.g. where to locate student halls

Question 4

To predict things organisations make decision based on several other factors but not all of them.. models are..

Answer 4

Simplified versions of the things they represent

Question 5

The more aspects a model covers, the more:

Answer 5

• Reliable it is

- The closer it is to reality

Question 6

Why do we use models?

Answer 6

• Less costly
• Can test things that are impossible
• Can give information quicker than real-world time

Question 7

What is a mathematical model?

Answer 7

A representation of a problem by a system of symbols and quantitative relationships or expressions

Question 8

In regards to maximising profit production what to these symbols mean: & ?

Answer 8

= for representing the number of bags to be produced

the total profit

Question 9

In regards to maximising profit production what to these symbols mean: & ?

Answer 9

= the number of bags to be produced

= the total profit

Question 10

How to work out profit?

Answer 10

P X Q

Question 11

What are decision variables?

Answer 11

Variables whose values are under our control and influence the performance of the system

Question 12

What is an objective function?

Answer 12

If the decision maker wants to maximise profit or minimise costs

Question 13

What are constraints?

Answer 13

Restrictions on the values of the decision variables

Question 14

In regards to maximising profit production what to these symbols mean: & ?

Answer 14

= the number of bags to be produced

= the total profit

Question 15

What are constraints?

Answer 15

Restrictions on the values of the decision variables

Question 16

What are the steps to constructing a linear programming model?

Answer 16

1. Identify the decision variables
2. Write the objectives
3. Write the constraints in terms of decision variables
4. Add the non-negativty constraints

e. g. Bag example
1) = number of bags to be produced
2) max⁡ = 10 ×
3) 5 × ≤ 40
4) ≥ 0

Question 17

In regards to maximising profit production what to these symbols mean: & ?

Answer 17

= the number of bags to be produced

= the total profit

Question 18

What are the steps to constructing a linear programming model?

Answer 18

1. Identify the decision variables: how many of something are they making (1 = . More than one = 2)
2. Write the objectives: max profit, min costs. Need to write: max P = (? the profit for the thing) x (, 1, 2). If more than one: max P = (?) x 1 + (?) x x2
3. Write the constraints in terms of decision variables:
4. Add the non-negativty constraints

e. g. Bag example
1) = number of bags to be produced
2) max⁡ = 10 ×
3) 5 × ≤ 40
4) ≥ 0

Question 19

What are the steps to constructing a linear programming model?

Answer 19

1. Identify the decision variables:
   - X1 = Number of …….
   - X2 = Number of …….
2. Write the objectives: max profit, min costs?
   - max P = (the profit for the thing) x (X1).
   - If more than one: z = (?) x X1 + (?) x X2 to maximise
3. Write the constraints in terms of decision variables:
   - (?How long they need in a certain area) x X1
   - Repeat the same for other constraints
   - Then add them together, and remember to add it needs to be less than the amount of hours available: (?) x 1 + (?) x 2 ≤.
   Repeat for all different constraints
4. Add the non-negativty constraints
   Whatever it is ≥0
   Have to do this for each :
   1 ≥ 0
   2 ≥ 0