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Chapter 6

1.2 Solving linear programming problems

In order to determine the production plan which maximises contribution,
the following 5 steps are employed.

Step 1: Define the variables each product will be given a letter in order
to simplify the calculations.

Step 2: Determine and state the objective function this will normally be
to maximise contribution and will be based on the contribution
per unit of each product.

Step 3: State the constraints each scarce resource/constraint will be
expressed as an equation based on the usage of each product
and the total of the resource available. There may also be other
constraints such a minimum of one product that must be
produced.

Step 4: Plot the constraints on a graph you will not be asked to do this
in the exam but you will be given a graph to interpret. An
example is shown on the next page.

Step 5: Find the optimal solution Using simultaneous equations,
calculate the coordinates of each vertex (furthest points) on the
feasible region. Then calculate the contribution (objective
function) at each vertex.

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