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

Multiple Choice

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 bitterness is a property measured as an index from 1 to 6 and a blend's bitterness is given by the weighted average (using the weight fraction of each beans in the blend as the weight) of the bitterness of individual beans going into the blend. Suppose that the bitterness indices for the three beans are respectively 2, 4, and 5 . A blend with bitterness in the range 3 to 4.5 is most desirable. The appropriate constraint/s will be

A) $2 X_{1}+4 X_{2}+5 X_{3} \geq 3.0$
B) $2 X_{1}+4 X_{2}+5 X_{3} \leq 4.5$
C) $2 X_{1}+4 X_{2}+5 X_{3} \geq 3.0$ and $2 X_{1}+4 X_{2}+5 X_{3} \leq 4.5$
D) the constraint/s are not correct since weights are not correctly represented