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In this problem, we provide a short preview of linear programming, which allows us to study linear inequalities in the same manner that the methods of Chapter 1 study linear equalities. We will begin by exploring the solutions to s 2 0 z 2 0 y+3z g 21 y+z g 9 2y+z g 14 Let R be the region in the (y, 2) plane where these relations hold. Question 1. Draw R. It will be convenient to rewrite our equations using socalled slack variables to be a combination of linear equalities and conditions of the form variable 2 0. In this case, we introduce variables ii, '1! and 21) dened by a = 213132 (1) v = 9yz w = 142yz So R is the region where u, 'v, w, y and z are positive. Question 2. Label the vertices of your drawing of R with their a, 'v, w, y and :5 values. Question 3. Rewrite the linear equations (1) in an extended matrix, ordering the variables as (a, v, w, y, 2). You should nd that your equations are in reduced row echelon form. Question 4. Reorder your variables as (gm/tum, z), (a, y, 11),\