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### Paper 1

LINEAR PROGRAMMING
(a) Solve linear programming problems by optimising a function in two variables, subject to one or more linear constraints, by numerical search along the boundary of the feasible region.
(b)Solve a system of linear equations to find the co-ordinates of the vertices of the feasible region.

Solve linear programming problems by optimising a function in two variables, subject to one or more linear constraints, by establishing optima by means of a search line and further comparing the gradients of the objective function and linear constraint boundary lines.

Clarification

• Candidates are expected to determine the optimal solution of a linear programming problem by substituting coordinates of the vertices of the feasible region into the objective function.
• Problems of the following types can be examined:
- Given the graphs and feasible region, determine the constraints and answer questions on the optimal function.
- Given the constraints, sketch the feasible region and answer questions on the optimal function.
- Given the problem situation and one constraint, determine the other constraints, sketch the feasible region and answer questions on the optimal function.
- Given the problem situation, determine all the constraints, sketch the feasible region and answer questions on the optimal function.
• Graph paper will be provided where necessary
• Constraints of the type:
ax + by ≤ c and
ax + by ≥ c
where a,b ≠ 0 will be limited to a maximum of 3.