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. Suppose that it is required to produce 200 pounds of coffee using this formulation. The appropriate constraint/s, given the definition of the problem and decision variables, will be A) $X_{1}+X_{2}+X_{3}=200$ B) $200 X_{1}+200 X_{2}+200 X_{3}200$ C) $200 X_{1}+200 X_{2}+200 X_{3}

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. Suppose that it is required to produce 200 pounds of coffee using this formulation. The appropriate constraint/s, given the definition of the problem and decision variables, will be
A) $X_{1}+X_{2}+X_{3}=200$
B) $200 X_{1}+200 X_{2}+200 X_{3}>200$
C) $200 X_{1}+200 X_{2}+200 X_{3}<200$
D) $X_{1}+X_{2}+X_{3}=1.0$ and multiply the answer by 200 to blend 200 pounds

Quizplus · Accepted Answer

The correct constraint to ensure that the blend of the three types of coffee beans makes up exactly 1 pound of coffee is $X_{1}+X_{2}+X_{3}=1.0$. To produce 200 pounds, this recipe would be scaled up by 200 times, but the fundamental constraint for the blend remains based on the proportions adding up to 1.0.

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 $X_{1}, X_{2}$