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Sem 5 Prep
← BI & Data ScienceLinear programming: turning a business problem into a model

Formulas for this chapter

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
Step 3 of 25
The real wordsTheory

The four parts of every model

The class writes them as numbered steps, and an exam answer should too.

1. Decision variablesThe quantities the manager wants to determine. Define them in words with units, e.g. x = number of tea cups made today.
2. Objective functionThe business goal as a linear expression in the variables, with Maximise or Minimise stated.
3. ConstraintsThe limits on available resources, one inequality each.
4. Non-negativityx, y greater than or equal to 0. You cannot make minus three cups.
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