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)?

  $1020

Step-by-step explanation:

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.

theres no picture: /

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.