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Svet_ta [14]
3 years ago
8

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.
Mathematics
1 answer:
boyakko [2]3 years ago
8 0

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:

2c+2l=20

c+3l=14

And total money raised can be shown by = 150c+175l

We have to maximize 150c+175l keeping in mind that 2c+2l \leq 20 and c+3l \leq 14

We will solve the two equations:  2c+2l=20 and c+3l=14

We get l = 2 and c = 8

And total money raised is 150\times8 + 175\times2 = 1200+350=1550 dollars.

Hence, Jayanta needs 2 labor union groups and 8 church groups.

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