Blending crude oil. a set of k different types of crude oil are blended (mixed) together in proportions θ1, . . , θk . these numbers sum to one; they must also be nonnegative, but we will ignore that requirement here. associated with crude oil type k is an n-vector ck that gives its concentration of n different constituents, such as specific hydrocarbons. find a set of linear equations on the blending coefficients, aθ = b, that expresses the requirement that the blended crude oil achieves a target set of constituent concentrations, given by the n-vector ctar . (include the condition that θ1 + · · · + θk = 1 in your equations.)