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 $125 from each church group and $200 from each neighborhood group, and she has a maximum of 16 hours of letter-writing time and a maximum of 14 hours of follow-up time available per month. Use the simplex method to complete parts (a) and (b). (a) Determine the most profitable mixture of groups Liz should contact and the most money she can raise in a month. Set up the linear programming problem. Let x, and x₂ represent the numbers of church groups and neighborhood groups, respectively, and let z be the total amount of money raised. Z= subject to 2x₁ + 2x₂ X₁ + 3x₂ x₁20, X₂ 20 (Do not factor. Do not include the $ symbol in your answers.) Liz can raise at most $ in a month. To raisk that amount, she should contact church group(s) and neighborhood group(s). (Type whole numbers.)