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)?
This is a standard linear programming problem, where we can apply the simplex method.
Applying the simplex method, we obtain these results:
0 0 1 3 5 16
0 0 2 1 8 20
0 9 -2 0 6 34
0 12 -8 -3 0 44
16 0 0 -7 -24 50
9 0 7 0 -3 800
8 0 8 1 0 1210
2 7 0 0 15 1300
4 6 0 -1 0 1470
0 60 10 0 1160
So, the minimum cost is $1160, which is obtained for 60 of Platter A and 10 of Platter B.
