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 to the right of the constraints): Constraint 4 700 Constraint 5 650 Solution > 560 500 3500