In formulating a coffee blending problem where there are three types of coffee beans, the objective is to find a recipe to make 1 pound of blended coffee that satisfies a set of properties at the least cost. The decision variables are $X_{1}, X_{2}$, and $X_{3}$, representing pounds (actually fractional pounds) of coffee beans used per pound of blended coffee. One of the constraints of the problem will be A) $X_{1}+X_{2}+X_{3}1.0$ C) $X_{1}+X_{2}+X_{3}=1.0$ D) no such constraint is required

Question

In formulating a coffee blending problem where there are three types of coffee beans, the objective is to find a recipe to make 1 pound of blended coffee that satisfies a set of properties at the least cost. The decision variables are $X_{1}, X_{2}$, and $X_{3}$, representing pounds (actually fractional pounds) of coffee beans used per pound of blended coffee. One of the constraints of the problem will be
A) $X_{1}+X_{2}+X_{3}<1.0$
B) $X_{1}+X_{2}+X_{3}>1.0$
C) $X_{1}+X_{2}+X_{3}=1.0$
D) no such constraint is required

Quizplus · Accepted Answer

The constraint $X_{1}+X_{2}+X_{3}=1.0$ ensures that the total weight of the coffee beans used equals exactly 1 pound, aligning with the goal of creating a 1-pound blend.

In Formulating a Coffee Blending Problem Where There Are Three X1,X2X_{1}, X_{2}X1​,X2​

In Formulating a Coffee Blending Problem Where There Are Three $X_{1}, X_{2}$