Liz is working to raise money for breast cancer research. She discovered that each church group requires 2 hours of letter writing and 1 hour of follow-up, while each neighborhood group needs 2 hours of letter writing and 3 hours of follow-up. Liz can raise $150 from each church group and $250 from each neighborhood group, and she has a maximum of 16 hours of letterwriting time and a maximum of 12 hours of follow-up time available per month. Use the simplex method to complete parts (a) and (b). E) (a) Determine the most protable mixture of groups Liz should contact and the most money she can raise in a month. Set up the linear programming problem. Let x1 and x2 represent the numbers of church groups and neighborhood groups, respectively, and let 2 be the total amount of money raised. X1 2 0, X2 2 0. (Do not factor. Do not include the $ symbol in your answers.) \fWrite the dual of the given minimization linear programming problem. Minimize C = 6y1 + 2y2 subject to y1 + 9y2 29 4y1 + 2y2 22 y1 , 12 20 . . . Form the dual problem. Maximize P= X 1 + X2 subject to X 1 + X2 S X1 + X2 S X1, X2 20State the dual problem for the given problem, but do not solve it. Minimize w = 7y1 + 2y2 + 4y3 subject to y1 + y2 + y3 26 y1 + y2 24 3y1 + 12 + 43 2 20 y1 20, y2 20, y3 20 . . . What is the dual problem? Maximize Z= subject to $7 $2 $4 X1 20, X2 20, X3 20