Verifying Linearity: Revisit Examples $2\mathrm{.}2,2\mathrm{.}3,$ and $2\mathrm{.}4$ and verify that the

properties of proportionality, additivity, and divisibility are reasonable assumptions in modeling each problem.Herrick Foods Company wishes to introduce packaged trail mix as a new product. The ingredients for the trail mix are seeds, raisins, flakes, and two kinds of nuts. Each ingredient contains a

certain amount of vitamins, minerals, protein, and calories; and the marketing department has

specified the product be designed so that a certain minimum nutritional profile is met. The

decision problem is to minimize the product cost and determine the product composition$$that

is$,$ by choosing the amount of each ingredient in the mix. The data shown below summarize the

parameters of the problem.

Grams per Pound Nutritional

Seeds Raisins Flakes Pecans Walnuts Requirement

Vitamins $102010302016$

Minerals $5749210$

Protein $14102115$

Calories $500450160300500600$

Cost$/$pound $$4$ $$5$ $$3$ $$7$ $$6$