Question

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

Explanation:

Step1: Define variables

Let $x$ = number of cappuccino bottles, $y$ = number of café au lait bottles.

Step2: Coffee usage constraint

Total coffee used ≤ 720 oz: $6x + 4y \leq 720$

Step3: Milk usage constraint

Total milk used ≤ 400 oz: $2x + 4y \leq 400$

Step4: Minimum production constraint

Total drinks ≥ 80: $x + y \geq 80$

Answer:

$x + y \geq 80$
$6x + 4y \leq 720$
$2x + 4y \leq 400$