a manufacturer produces two types of bottled coffee drinks: cappuccinos and cafés au lait. each bottle of…

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 other than x≥0 and y≥0. x + y≥80 0.4x + 0.5y≥100 6x + 4y≤720 2x + 4y≤400 6x + 2y≥720 4x + 4y≥400 done

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 other than x≥0 and y≥0. x + y≥80 0.4x + 0.5y≥100 6x + 4y≤720 2x + 4y≤400 6x + 2y≥720 4x + 4y≥400 done

Answer

Explanation:

Step1: Analyze coffee - quantity constraint

The manufacturer has 720 ounces of coffee available. Each cappuccino ($x$) requires 6 ounces of coffee and each café au lait ($y$) requires 4 ounces of coffee. So the coffee - quantity constraint is $6x + 4y\leq720$.

Step2: Analyze milk - quantity constraint

The manufacturer has 400 ounces of milk available. Each cappuccino ($x$) requires 2 ounces of milk and each café au lait ($y$) requires 4 ounces of milk. So the milk - quantity constraint is $2x+4y\leq400$.

Step3: Analyze production - quantity constraint

The manufacturer must produce at least 80 coffee drinks each day. So $x + y\geq80$.

Answer:

$x + y\geq80$, $6x + 4y\leq720$, $2x + 4y\leq400$