The Highly Improbable Foods Company makes vegetarian versions of burgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of one burger, three hot dogs, and $5$ chicken wings, which costs $\$16.$ Platter B consists of two burgers, one hot dog, and $8$ chicken wings, which costs $\$20.$

A picnic organizer requires $80$ hamburgers, $95$ hot dogs, and $380$ chicken wings. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?

Let x and y represent the numbers of Platter A and Platter B the organizer needs to purchase, respectively. The given conditions can be summarized as ...

x + 2y ≥ 80 . . . . . . 80 or more hamburgers are required

3x + y ≥ 95 . . . . . . 95 or more hot dogs are required

5x +8y ≥ 380 . . . . 380 or more chicken wings are required

16x +20y = c . . . . . c must be minimized

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It is useful to graph these inequalities, and look for the vertex of the feasible region that is closest to the origin. That vertex is (x, y) = (20, 35). The other vertex that is close to the origin is (60, 10). The cost of that order would be $1310.

The value of an order of 20 Platter A and 35 Platter B is ...

20×$16 +35×$20 = $320 +700 = $1020

The minimum cost of the picnic food is $1020.