A manufacturer produces two types of bottled coffee drinks: cappuccinos and cafés au lait. Each bottle of cappuccino requires 6 ounces of coffee and 2 ounces of milk and earns a profit of $0.40. Each bottle of café au lait requires 4 ounces of coffee and 4 ounces of milk and earns a profit of $0.50. The manufacturer has 720 ounces of coffee and 400 ounces of milk available for production each day. To meet demand, the manufacturer must produce at least 80 coffee drinks each day. Let x = the number of cappuccino bottles and y = the number of café au lait bottles. Identify the constraints on the system.
x+y>=80
6x+4y<=720
2x+4y<=400
x+y>=80
6x+4y<=720
2x+4y<=400
To identify the constraints on the system, we need to consider the limitations or restrictions given in the problem.
1) Coffee Constraint: The manufacturer has 720 ounces of coffee available each day. Each cappuccino bottle requires 6 ounces of coffee, and each café au lait bottle requires 4 ounces of coffee. Therefore, the coffee constraint can be expressed as:
6x + 4y ≤ 720
2) Milk Constraint: The manufacturer has 400 ounces of milk available each day. Each cappuccino bottle requires 2 ounces of milk, and each café au lait bottle requires 4 ounces of milk. Therefore, the milk constraint can be expressed as:
2x + 4y ≤ 400
3) Production/Demand Constraint: The manufacturer must produce at least 80 coffee drinks each day. The total number of coffee drinks can be calculated by adding the number of cappuccino bottles (x) and the number of café au lait bottles (y). Therefore, the production/demand constraint can be expressed as:
x + y ≥ 80
These three constraints represent the limitations on the system based on the available coffee, milk, and production requirements.