You've formulated an optimization problem in traditional linear programming form and would like to use Excel to solve the problem.
Use Solver's linear optimization capabilities.
Linear optimization problems can be written in the form of an objective function to maximize (or minimize) subject to constraints. Constraints can be written in the form of inequalities or equalities. Consider this simple example:
If this were a product mix type of problem, the variables x 1 and x 2 could represent different products subject to some availability or production constraints, while the objective function could represent total profit given the mix of products produced. The idea is to find the optimum mix of products so as to maximize profit. Linear optimization is not limited to this sort of product mix problem. For example, your problem could consist of trying to maximize the vitamin content of a livestock feed given certain ingredients, subject to their availability and cost. Or your problem could consist of trying to minimize the cost of labor for producing certain products in your laboratory (see the next recipe for a hypothetical example).
Moreover, the problem need not be limited to ...