LEARNING OBJECTIVE: To revise solving Linear programming problems
SUCCESS CRITERIA: Full marks on Linear Programming exam Questions
LESSON:
Stages in solving a linear programming question
Step 1: Find the objective function – NB DO NOT SIMPLIFY, YOU MIUST USE THE WORDS MINIMISE OR MAXIMISE
Step 2: List all the constraints _SIMPLFY TO LOWEST WHOLE NUMBERS, DO NO FORGET TO STATE WHEN VARIABLES CAN ONLY BE POSITIVE ( ie number of items built/sold/carried...)
Step 3: Plot all Constraints on a suitable graph – ENSURE SCALES ARE AS BIG AS POSSIBLE TO FILL THE GRAPH PAPER YOPU HAVE BEEN GIVEN- LABEL ALL LINES (ALONG LINES MAKES IT EASIER TO SEE EXTEND BEYOND ACCESS TO MAKE CLEARER IF NECCESARY)
STEP 4 – FIND APPROPRIATE VERTEX
Method 1 – Using Objective function
Plot objective function then use this to find min of max vertex
REMEMBER – Min vertex is first vertex objective function hits when moving towards the region
Max Vertex is last vertex as objective function moves out of region
Find exact cords using simultaneous equations between to two constraint lines that meet at the vertex.
Substitute cords of this vertex into Objective function to find Max/Min value
Method 2 – Exhaustive method – finding all vertices
Find the cords of ALL vertices using simultaneous equations / reading off graph if integer values, put these into a table
For each vertex substitute values into objective function to work out value at that vertex.
Once ALL vertices have been completed you can read off from your table the max, or min values –DONT FORGET TO STATE THE SOLUTION – ie the number of each variable needed, as well as the max.min value generated (ie cords of chosen vertex)
INTEGER ONLY VALUE
If question states (Or implies ) integer values and you have got a vertex with non integer cords you must find the nearest pair of integer cords that satisfy ALL constraints and give the max/min value – this is best done in a table
Homework 1
Homework 2
Use above examples to demonstrate above task list
