The LP model template
Maximise (or Minimise) Z = c1 x1 + c2 x2 + ... + cn xn
subject to a11 x1 + a12 x2 + ... <= b1
a21 x1 + a22 x2 + ... <= b2
x1, x2, ..., xn >= 0
Every formulation question. Write the four blocks in this order: variables in words, objective with direction, one line per constraint, non-negativity.
- xj
- Decision variable j, defined in words with units
- cj
- Objective coefficient: profit or cost per unit of xj
- aij
- Amount of resource i used by one unit of xj
- bi
- Amount of resource i available, the right-hand side
Corner point of two constraints
Solve the two boundary equations simultaneously:
a11 x + a12 y = b1
a21 x + a22 y = b2
Subtract when a term matches; else substitute.
Listing the corners of a two-variable feasible region. Discard any intersection that violates another constraint or non-negativity.
- b1, b2
- Right-hand sides of the two constraints
- (x, y)
- The candidate corner point
Slack and surplus
slack = RHS - LHS (for a <= constraint)
surplus = LHS - RHS (for a >= constraint)
Binding <=> slack = 0
After solving, to say which resource limits the business. Solver's Answer Report prints this column for you.
- LHS
- Left-hand side evaluated at the optimal solution
- RHS
- The stated limit