Let x, y, z, and w represent the population in millions of four cities A, B, C, and B, respectively. Express the given statement as an equation in X, y, z, and w. If the equation is linear, express it in the standard form ax + by + :2 + dw = k. (If the equation is not linear, enter NONLINEAR.) City A has six times as many people as cities B and C combined. NONLINEAR X Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer using the parameters x, y, and/or z.) X + V + 67 = 7 =1 + Z = 0 N ( x , y, Z ) = -8, - 9,4 XSolve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.) Maximize p = x + y + 2z subject to x + 2y + 2z = 80 2x + y + 3z s 80 x 20, y 20, 2 20. P = 11 (x, y, Z) = 1,2,0 XNutrition Ra, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of Fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 246 grams of protein and at least 156 grams of fat. If chicken costs 90. per ounce and grain costs 11: per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost? (If an answer does not exist, enter DNE.) grain Ex oz chicken x o2 Find all solutions of the given system of equations and check your answer graphically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).) 4x - 2y = 3 8x - 4y = 3 (x, y) = NO SLUTON XFind all solutions DFthe given system of equations and Check your answer graphically. [If there is no solution, enter ND SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).} 5x+ 7y=3 _x_7 __3 5y_ 5 (m) =( NO SOLUTION ) x