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 The objective maximizes 75X1 + 90X2 The objective minimizes 4X1 + 10X2 The objective is always a 1000 The objective maximizes 2X1 + 5X2

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

The objective of the tea blending problem is to minimize the total cost of the blend while meeting quality standards and other problem constraints. The correct statement is that the objective minimizes 2X1 + 5X2.

Step-by-step explanation:

The objective of the tea blending problem is to minimize the total cost of the blend while meeting quality standards and other problem constraints. The cost per pound and available pounds of each type of tea leaf are given, along with the taste and aroma ratings for each type of tea. To formulate a linear programming problem, we define the decision variables as X1 and X2, representing the pounds of type 1 and type 2 tea used in the blend, respectively. The objective function in this case is to minimize the cost, which is given by the expression 2X1 + 5X2. Therefore, the correct statement is: The objective minimizes 2X1 + 5X2.