D1, C6 - Linear Programming Flashcards
With linear programming, what is another term for variables (x, y, z, …)
Decision variables
With linear programming, what is another term for inequalities (5x + 2y >= 10)
Constraints
With linear programming, what is the area inside all the constraints called
The feasible region
With linear programming, what is another term for minimising cost / maximising profit (P = 2x - 3y, C - 7x + 3y)
The objective function
What is the solution to a linear programming problem called
The optimal solution
From the statements given in linear programming questions, what do you first write down
Constraints
Objective function
What must you specify as an additional constraint for each of the variables
Non-negativity
If they can be below 0
You will need twice as many pocket diaries as desk top diaries. How do you write this as an inequality
Assign variables:
pocket = y
desk top = x
y needs to be at least twice as big as x
So if 2x = y
ans –> 2x <= y
For linear programming how would you write percentages
As decimals
Syrup A contains 50% fruit and syrup B contains 35% fruit. When mixed the syrup C must contain at least 40% fruit, how do you write this as an inequality
0.5x + 0.35y >= 0.4(x + y)
0.5x + 0.35y >= 0.4x + 0.4y
0.1x >= 0.05y
2x >= y
What part of the liner programming graph do you shade
Unwanted areas
What letter do you denote as the feasible region on a graph
R
Are less than (<) and more than (>) dotted or solid lines
Dotted
Are less than or equal to (<=) and more than or equal to (>=) dotted or solid lines
Solid
Where are minimising or maximising solutions found on linear programming graph
At once of the vertices of the feasible region polygon (R)
What are the 2 methods for finding the minimising or maximising solutions on a linear programming graph
Ruler-line method
Vertex-testing method
How would you perform the ruler line method to maximise or minimise P = 5x + 2y
1) Replace P with any non-zero positive number e.g. 10, 20, 30, etc
2) More your ruler perpendicular to the line in the equation created
3) First vertex is the minimal solution, last vertex is the maximum solution
With the ruler-line method, what solution is the first vertex reached
Minimise point
With the ruler-line method, what solution is the last vertex reached
Maximise point
How do you perform the vertex-testing method to find the minimising or maximising point
1) Solve the intersection of lines simultaneously to find the coordinates of all the vertices
2) Substitute all these solutions into the objective function
3) Lowest answer is minimised points, biggest answer is maximised point
What letter denotes maximising profit on sales
P
What letter denotes minimising production costs
C
What happens if the objective line is parallel to the final constraint line it will hit
There will be two vertices it reaches last at the same time
All points on the line the objective line is parallel to will be optimal points
Why may we need integer solutions to linear programming problems
Non-integer solutions may not be practical or feasible e.g. cannot have a fraction of a person
How would you find the integer solution if the optimal point is (16 and a third, 20 and 2 fifths)
1) Draw a box with each integer point around the optimal point (16,20)(17,20)(16,21)(17,21)
2) Reject any integer points that are clearly not in the feasible region
3) If it is not clear test each point against the constraints to see if it in feasible region, if not reject it
4) Test the remaining points in the objective function to find which integer point maximises (or minimises)
