Question

The Coastal Tea Company sells 60-pound bags of blended tea to restaurants. To be able to label the tea as South Carolina Tea, at least 55% of the tea(by weight) in the bag must be Carolina grown. For quality, Coastal requires that the blend achieve an average aroma rating of at least 1.65. Carolina tea, which costs Coastal $1.80 per pound, has an aroma rating of 2; other teas likely to be blended with Carolina tea are only rated at 1.2, but they are available for only $0.60 per pound.

The best mix of Carolina and regular tea to achieve Coastal’s blending goals, while keeping the costs as low as possible is:

Answer 1

To achieve Coastal Tea Company's blending goals, the best mix of Carolina and regular tea is 38 pounds of Carolina tea and 22 pounds of regular tea.

Step-by-step explanation:

To determine the best mix of Carolina and regular tea, we need to consider both the percentage of Carolina tea and the cost of the blend. Let's assume that x represents the weight of Carolina tea in the blend, in pounds. The weight of regular tea in the blend would then be (60 - x) pounds.

We need to find the minimum value of x that satisfies two conditions: the Carolina tea must make up at least 55% of the blend, and the average aroma rating of the blend must be at least 1.65.

The equation that represents the percentage condition is: (x/60) * 100 >= 55. This simplifies to x >= (55/100) * 60 = 33 pounds.

The equation that represents the aroma rating condition is: (2x + 1.2(60 - x))/60 >= 1.65. Solving this inequality, we find that x >= 37.2 pounds.

The minimum value of x that satisfies both conditions is 37.2 pounds. However, since the weight must be a whole number, we round up to 38 pounds. Therefore, the best mix of Carolina and regular tea would be 38 pounds of Carolina tea and (60 - 38) = 22 pounds of regular tea.