Formulate the problem of maximizing the bar\'s profit as a linear programming pr

Question

Formulate the problem of maximizing the bar's profit as a linear programming problem. DO NOT SOLVE.

The bartender of your local pub has asked you to assist him in finding the combination of mixed drinks that will maximize his revenue. He has the following bottles available: i quart (32 oz.) Old Cambridge (a fine whiskey-cost $8/quart) l quart Joy Juice (another fine whiskey-cost $10/quart) 1 quart Ma's Wicked Vermouth ($10/quart) 2 quarts Gil-boy's Gin (S6/quart) Since he is new to the business, his knowledge is limited to the following drinks: Whiskey Sour Price $1 Manhattan Martini Pub Special 2 oz. whiskey 2 oz. whiskey I oz. vermouth 2 oz. gin $%2 $2 $3 1 oz, vermouth 2 oz. gin 2 oz. whiskey

Explanation / Answer

1) LP model is as follows

Decision variables:

X1 = Number of servings to make of Whiskey Sour

X2 = Number of servings to make of Manhattan

X3 = Number of servings to make of Martini

X4 = Number of servings to make of Pub Special

Max 1X1 + 2X2 + 2X3 + 3X4

s.t.

2X1 + 2X2 + 2X4 <= 64 (Available fine whiskey Old Cambridge and Joy juice)

1X2 + 1X3 <= 32 (Ma's wicked vermouth)

2X3 + 2X4 <= 64 (Gil-boy's gin)

X1, X2, X3, X4 >= 0

2) The problem in canonical form is as follows

Max 1X1 + 2X2 + 2X3 + 3X4 + 0s1 + 0s2 + 0s3

s.t.

2X1 + 2X2 + 0X3 + 2X4 + 1s1 + 0s2 + 0s3 = 64

0X1 + 1X2 + 1X3 + 0X4 + 0s1 + 1s2 + 0s3 = 32

0X1 + 0X2 + 2X3 + 2X4 + 0s1 + 0s2 + 1s3 <= 64

X1, X2, X3, X4 >= 0

3) Solution of the problem using simplex method is as follows:

4) Solution is

x1 = 0

x2 = 16

x3 = 16

x4 = 16

Objective value = 112

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