Question

29 A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup of 2% milk, frothed, and 0.5 cup of whipped cream. The low-fat latte contains a shot of espresso, 1.25 cups of skim milk, frothed, and no whipped cream. The plane begins its journey with 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream. The airline makes a profit of $1.58 on each regular

Answer 1

Step 1 formulation
Decision variables	Let the number of regular lattes sold be 'x'
	Let the number of Low-fat lattes sold be 'y'
Objective Equation	Maximize Profit = 1.58x + 1.65y
Espresso constraint equation	1x + 1y < 100
Skim Milk constraint equation	1.25y < 60
2% Milk constraint equation	1x < 60
Whipped cream constraint equation	0.5x < 30

	Regular	LowFat
Number of units	x	y
Profit	1.58x	1.65y
Constraints
Espresso	1x	1y	1x + 1y	<	100
Skim Milk	0	1.25y	1.25y	<	60
2% Milk	1x	0	1x	<	60
Whipped cream	0.5x	0	0.5x	<	30
			LHS	Sign	RHS

Therefore, the ideal mix would be 52 regular lattes and 48 low-fat lattes.

	Regular	LowFat
Number of units	52	48
Profit	82.16	79.2	161.36
Constraints
Espresso	52	48	100	<	100
Skim Milk	0	60	60	<	60
2% Milk	52	0	52	<	60
Whipped cream	26	0	26	<	30
			LHS	Sign	RHS