the variable you want to maximise or minimise (P) = each variable times the amount of P the contribute
e.g. maximise money earned
x=£3
y=£2.50
z=£4
(MAX)P=3x+2.5y+4z is the objective function
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It is usually the answer in linear programming. The objective of linear programming is to find the optimum solution (maximum or minimum) of an objective function under a number of linear constraints. The constraints should generate a feasible region: a region in which all the constraints are satisfied. The optimal feasible solution is a solution that lies in this region and also optimises the obective function.
A linear function is called "linear" because it represents a straight line. To graph a linear function, find two points that satisify that function, plot them, and then draw a straight line between them.
A linear function is increasing if it has a positive slope. To find this easily, put the function into the form y=mx+b. If m is positive, the function is increasing. If m is negative, it is decreasing.
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Given a linear function in n variables, you need to select values for (n-1) of the variables. Solve the resulting function for the nth variable. Then the ordered n-tuple represents the coordinates, in n-dimensional space, of a point that is on the linear function.Selecting different sets of (n-1) variables, and different values will result in different solutions. Together, these will from a line in n-dimensional space.