Chapter 6: planning with limiting factors

Question 1

What is the aim of key factor analysis?

Answer 1

max profit

Question 2

What are the 5 steps of key factor analysis?

Answer 2

Step 1: identify the scarce resource
Step 2: Calculate the contribution per unit for each product
Step 3: Calc the contribution per unit of the scarce resource for each product
Step 4: rank the products in order of the contribution per unit of the scarce resource
Step 5: allocate resources using this ranking & answer the question

Question 3

When can key factor analysis be used

Answer 3

1 scarce resource

Question 4

When is linear programming used

Answer 4

2 or more scarce resources

Question 5

What is linear programming used for

Answer 5

Max contribution and/or min costs

Question 6

How to formulate linear programming?

Answer 6

Step 1: define the variables

Step 2: Define & formulate objective (y=mc+c)

Step 3: Formulate constraint

Step 4: Draw a graph identifying the feasible region

Step 5: solve for the optimal production plan

Step 6: Answer question e.g max profit= ?

Question 7

How to identify the feasible region

Answer 7

Shown by the <and equal to (black line vs dotted line) above and below the line etc…

Question 8

What are the 2 stages of finding the optimal solution

Answer 8

1) By inspection - it will lie on the corner of the feasible region. Calc the contribution at each corner (not to do in the exam- time consuming)

2) Drawing an iso-contribution line- line where all points represent an equal contribution

or simultaneous equations

Question 9

Assumptions of limiting factor analysis

Answer 9

1) single quantifiable objective- can have multiple objectives e.g max return min risk

2) each product uses same amount of scarce resource per unit

3) contribution/unit is constant-economies of scale= discount for bulk buy or selling price lowered to sell more

4) products are independent- can buy 2 products together/ they can be manufactured jointly

5) scenario is ST- can ignore Fixed costs

Question 10

What is slack

Answer 10

Amount in which a resource is under-utilised or a product with unfulfilled demand
On a graph the optimum point doesn’t fall on a given resource line

Question 11

What is the solution to slack

Answer 11

When 2 critical constraint lines cross- they’ll be fully utilised

Question 12

Why is slack important

Answer 12

Critical constraints (0 slack)= gaining additional units of the scarce resource= optimal solution improved. If another department wants the resources= lower contribution

Non-critical constraints= gaining or losing a small no of units has no impact on optimal solution

Question 13

What is the shadow/dual price?

Answer 13

increase in contribution created by the availability of 1 additional unit of the limiting factor at original cost
Max premium the firm is willing to pay for 1 extra unit of each constraint

Non-critical constraints have 0 shadow price as slack exists already

Question 14

How to calculate the shadow price

Answer 14

Step 1: take the equations of the straight lines that intersect at the optimal point. Add 1 unit to the constraint concerned and leave the other unchanged

Step 2: use simultaneous equations to derive a new optimal solution

Step 3: Calc the revised optimal contribution&
compare to the original contribution cancelled
Increase is the shadow price

Question 15

What are the implications of shadow pricing?

Answer 15

Could negotiate a lower than shadow price
If a critical constraint is obtained the constraint line moves outwards (changing shape of the region). After a period of time it won’t be worth buying more scarce resource as non-critical constraints become critical