Jayanta is raising money for the? homeless, and discovers each church group requires 2 hr of letter writing and 1 hr of? follow-up calls, while each labor union needs 2 hr of letter writing and 3 hr of ?follow-up. She can raise ?$150 from each church group and ?$175 from each union. She has a maximum of 20 hours of letter writing and 14 hours of ?follow-up available each month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month.

Answer:Jayanta needs 2 labor union groups and 8 church groups.Step-by-step explanation:Let c denotes churches .Let l denotes labor unions.We know that Jayanta can only spend 20 hours letter writing and 14 hour of follow-up. So, equations becomes:[tex]2c+2l=20[/tex][tex]c+3l=14[/tex]And total money raised can be shown by = [tex]150c+175l[/tex]We have to maximize [tex]150c+175l[/tex] keeping in mind that [tex]2c+2l \leq 20[/tex] and [tex]c+3l \leq 14[/tex] We will solve the two equations:  [tex]2c+2l=20[/tex] and [tex]c+3l=14[/tex]We get l = 2 and c = 8And total money raised is [tex]150\times8 + 175\times2[/tex] = [tex]1200+350=1550[/tex] dollars.Hence, Jayanta needs 2 labor union groups and 8 church groups.