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The Very Possible Foods Company makes vegan versions of hamburgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of 1 burger, 3 hot dogs, and 5 chicken wings, which costs $16. Platter B consists of 2 burgers, 1 hot dog, and 8 chicken wings, which costs $20.

 

 A barbecue 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)?

 May 18, 2020
 #1
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-1

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.

 May 18, 2020
 #2
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0

Well, your "simplex method" didn't work very well !!!.

 

The cheapest deal is as follows: 35 Platter B  x  $20 =$700, which will give you: 70 burgers, 35 dogs and 280 C, wings.

                                                    20 Platters A x $16 =$320, which will give you: 20 burgers, 60 dogs and 100 C. wings.

                                                                   Total cost =$1020, which will give you: 90 burgers, 95 dogs &  380 C, wings.

 May 18, 2020
 #3
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+1

It is $1,020. 

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

__

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. This is from the site Brainly!!! 

This is where I got it: https://brainly.com/question/15019280

 May 27, 2020

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