Applications - A Guide to MATLAB for Beginners and Experienced Users - page 173

Effect of increases in demand for each of the 3 sectors
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Linear Programming

MATLAB is ideally suited to handle linear programming problems. These
are problems in which you have a quantity, depending linearly on several
variables, that you want to maximize or minimize subject to several
constraints that are expressed as linear inequalities in the same variables. If
the number of variables and the number of constraints are small, then there
are numerous mathematical techniques for solving a linear programming
problem — indeed these techniques are often taught in high school or
university courses in finite mathematics. But sometimes these numbers are
high, or even if low, the constants in the linear inequalities or the object
expression for the quantity to be optimized may be numerically
complicated — in which case a software package like MATLAB is required to
effect a solution. We shall illustrate the method of linear programming by
means of a simple example, giving a combination graphical-numerical
solution, and then solve both a slightly and a substantially more complicated
problem.
Suppose a farmer has 75 acres on which to plant two crops: wheat and
barley. To produce these crops, it costs the farmer (for seed, fertilizer, etc.)
$120 per acre for the wheat and $210 per acre for the barley. The farmer has
$15,000 available for expenses. But after the harvest, the farmer must store
the crops while awaiting favorable market conditions. The farmer has