Chapter 6 - Planning with limiting factors

Question 1

What are the steps when planning with one limiting factor?

Answer 1

Step 1: Identify the scarce resource
Step 2: Calculate the contribution per unit of each product
Step 3: Calculate 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 the resources using this ranking and answer the question

Question 2

If 2 or more resources are in short supply what is required?

Answer 2

linear programming

Question 3

What is linear programming used for?

Answer 3

• maximizing contribution
• minimise cost

Question 4

What is the iso contribution line?

Answer 4

line where all points represent an equal contribution

Question 5

What are the steps to find the optimal production plan?

Answer 5

Step 1: Define the variables
Step 2: Define and formulate the objective function
Step 3: Formulate the constraints
Step 4: Draw a graph identifying feasible region
Step 5: Solve the optimal production plan
Step 6: answer question

Question 6

What is slack?

Answer 6

the amount by which a resource is under-utilized, i.e., slack occurs when the maximum availability of a resource is not used.h

Question 7

Why is slack important?

Answer 7

• for critical constraints (0 slack), then gaining additional units of these resources will allow the optimal solution to be improved (e.g., higher cont earned).

Question 8

What is the shadow or dual price of a limiting factor?

Answer 8

the increase in contribution created by the availability of one additional unit of the limiting factor at the original cost

Question 9

What does the shadow price represent?

Answer 9

the max premium that the firm should be willing to pay for one extra unit of each constraint

Question 10

Will non-critical constraints have a shadow price?

Answer 10

no because slack already exists

Question 11

What are the steps to calculate shadow pricing?

Answer 11

Step 1: take the straight line equations and add one unit of the constraint leaving the other unchanged
Step 2: Use simultaneous equations to derive a new optimal solution
Step 3: Calculate the revised optimal contribution and compare to the cont calculate. The increase is the shadow price