Problem 1 Soylent Diet Planning. Recall the LP from Problem 1.a of homework 1: Maximize0.1xB+0.25xR+0.2xYs.t.25xB+110xR+72xY15000.1xB+2.2xR+0.65xY206.3xB+1.8xR+4.1xY100xB+xR+xY=30xB,xR,xY0 (a) Rewrite the LP in standard equality form (b) Rewrite the LP in matrix equality form. That is, identify the matrix A and vectors b and c so that the following LP is equivalent to our problem. Maximizes.t.cxAx=bx0 (Hint: Our problem has four constraints and six variables (including slack); thus A should be a 46 matrix, b should be a 14 vector, and c should be a 16 vector.) (c) Notice that your A matrix from part (b) is not in the canonical form for any feasible basis. For now, let B={s1,s2,s3,xY} and N={xB,xR} be the target basis and compute the canonical form of the constraints. (d) Identify the basic solution and objective function value associated with the new basis