Bob is preparing for a party, and he expects lots of hungry guests. He has the f

Question

Bob is preparing for a party, and he expects lots of hungry guests. He has the following ingredients on hand:

MEAT

AMOUNT ON HAND (ounces)

Turkey

57

Roast Beef

62

Ham

51

Bob decides make 4 different types of sandwich for the party: Roast Beef, Turkey/Ham, Bob Special, and Turkey. Each sandwich has 4 ounces of meat in total. A Turkey/Ham sandwich is ½ turkey and ½ ham. A Bob special has equal parts of all 3 meats. He has tons of bread and cheese on hand, so the number of sandwiches he can create is limited by the amount of meat he has on hand. Bob wants to create as many sandwiches as possible, while making at least 4 of each type of sandwich. He knows that some of his friends will want to try the Bob special, so he wants to make sure that at least 1/4 of the total number of sandwiches prepared are Bob specials. How many sandwiches of each type should he produce?

MEAT

AMOUNT ON HAND (ounces)

Turkey

57

Roast Beef

62

Ham

51

Explanation / Answer

Let say there are X amount of Roast beef sandwich, Y number of Turkey/Ham sandwich, Z number of Bob special and W number of Turkey sandwich. SO, a turkey/ham sandwich require 2 ounces of turkey and 2 ounces of ham. Similarly, a bob special sandwich requires 4/3 ounces of each type of meat.

Maximize : X + Y + Z + W

Constraint to :

X, Y, Z, W >= 4

2Y + 4Z/3 + 4W <= 57 ...(i)

4X + 4Z/3 <= 62 ...(ii)

2Y + 4Z/3 <= 51...(iii)

Z >= 1/4 * (X + Y + Z + W)

3Z >= X + Y + W

X + Y - 3Z+ W <= 0

X,Y,Z,W all are integers.

By solving the given problem with excal solver.

The answer i got is given below.

THe maximum number of sandwiches = 39

where number of Roast Beef = 11

Number of Ham/Turkey = 11

Bob special = 13

Turkey = 4

The final result solution is

Target Cell (Max) Cell Name Original Value Final Value $K$2 Maximize Value 0 39 Adjustable Cells Cell Name Original Value Final Value $C$1 X 0 11 $E$1 Y 0 11 $G$1 Z 0 13 $I$1 W 0 4 Constraints Cell Name Cell Value Formula Status Slack $K$3 Constraint Value 11 $K$3>=$J$3 Not Binding 7 $K$4 Value 11 $K$4>=$J$4 Not Binding 7 $K$5 Value 13 $K$5>=$J$5 Not Binding 9 $K$6 Value 4 $K$6>=$J$6 Binding 0 $K$7 Value 55.33333333 $K$7<=$J$7 Not Binding 1.666666667 $K$8 Value 61.33333333 $K$8<=$J$8 Not Binding 0.666666667 $K$9 Value 39.33333333 $K$9<=$J$9 Not Binding 11.66666667 $K$10 Value -13 $K$10<=$J$10 Not Binding 13 $C$1 X 11 $C$1=integer Binding 0 $E$1 Y 11 $E$1=integer Binding 0 $I$1 W 4 $I$1=integer Binding 0 $G$1 Z 13 $G$1=integer Binding 0

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