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Chapter 13 Linear Programming

Optimize an object function (profit, revenue or cost), subject to certain constraints

Eg. Maximize profit, or minimize cost

If the function to be minimized or maximized is linear, then calculus does us no good.

Constraints are generally inequality that restrict the possible values of the variables

Nonnegativity constraint

  1. The Top Brass Company makes large championship trophies for youth athletic leagues.  At the moment they are planning production for fall sports: football and soccer.  Each football trophy has a wood base, an engraved plaque, a large brass football on top and returns $12 in profit.  Soccer trophies are similar except that the brass soccer ball is on top and the unit profit is only $9.  Since the football has an asymmetric shape, it’s base requires 4 board feet of wood; the soccer base requires only 2 feet of wood.  At the moment, there are 1000 brass footballs in stock, 1500 soccer balls, 1750 plaques, and 4800 board feet of wood.  What trophies should be produced from these supplies to maximize total profit, assuming that all that are made can be sold?


 – object function

  = constraints

Feasible solution is a solution that satisfies all the constraints

Optimal solution is feasible and is the minimum or maximum value of the function

Infeasible = cannot satisfy all the constraints at the same time = no solution

Shadow Price is the amount the profit (objective function value) will be altered if I increase (or decrease) the amount of the constraint.

Objective function: maximize the number of people we reaching with advertising

Subject to the following constraints:

SolverTable – an add-on to Solver – written by textbook author

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