Question

Answer the following question with respect to the tea blending problem posted in Canvas (Test 6 Output document above). Which of the following statements is true? Group of answer choices 2X1 + 5X2 ≥ 80 is a constraint X1 + X2 ≥ 80 is a constraint [(75X1 + 80X2)/(X1+X2)] ≥ 1000 is a constraint [(70X1 + 80X2)] ≥ 75000 is a constraint

Management Science Test OUTPUTS 1. THE TEA BLENDING PROBLEM EASYT manufactures tea by blending two kinds of tea leaves Type 1 and Type 2. The cost per pound and the available pounds of each type of tea leaf are stated below. Leaf type Cost per pound Available pounds Type 1 $2 700 Type 2 $5 550 Consumer tests were used to provide ratings on a scale of 1-100 with higher ratings indicating higher quality. Product quality ratings require at least a minimum rating of 80 for TASTE and a minimum rating of 75 for AROMA. The individual taste and aroma ratings for the two types of tea are as below. Leaf type TASTE RATING AROMA RATING Type 1 75 70 Type 2 90 80 Assume that aroma and taste attributes will be a weighted average of the attributes of the tea leaves (types) used in a blend. Assume the following: a) A 1000 pounds of blended tea is to be produced using the minimum quality for taste and aroma. b) X1 = pounds of type 1 tea used in the blend c) X2 = pounds of type 2 tea used in the blend Formulate a linear programming problem to identify the pounds of Type 1 and Type 2 teas to be blended, in order to minimize total cost of the blend, while meeting quality standards and any other problem constraints. The above problem was also solved with some Linear Programming solver and a portion of the constraint set (along with optimal solution values in BLUE) is shown (the dual variables are also in blue t

Answer 1

None of the provided constraint statements accurately reflect the constraints for the tea blending problem. Valid constraints would involve the cost, taste and aroma ratings, the blend's weight, and quality standards.

Step-by-step explanation:

To determine which constraint is correct for the tea blending problem, we need to relate the information given in the scenario to quantities and ratings of tea leaves. The problem involves minimizing the cost of blending tea while meeting quality standards for taste and aroma. With X1 being the pounds of type 1 tea and X2 the pounds of type 2 tea, we look into the statements given:

1. 2X1 + 5X2 ≥ 80 is not explicitly stated as a constraint in the given context and does not match the cost or quality requirements.
2. X1 + X2 ≥ 80 does not directly relate to the context of the problem, as it does not take into account the taste and aroma ratings or the costs.
3. [(75X1 + 80X2)/(X1+X2)] ≥ 1000 is not a valid constraint given the ratings and targeted blend weight, as it implies an average rating that does not make sense in this context.
4. [(70X1 + 80X2)] ≥ 75000 uses the aroma ratings for each tea type with an arbitrary number that doesn't correlate with the information given.

None of the provided statements reflect an accurate constraint based on the problem data related to cost, quality ratings, or the goal of blending 1000 pounds of tea. However, constraints would likely relate to the minimum quality ratings of 80 for taste and 75 for aroma based on a weighted average of X1 and X2, and the availability of 700 pounds and 550 pounds of each type of leaf respectively, as well as the goal to minimize cost.