Liz is working to raise money for breast cancer research by sending informational letters to local neighborhood organizations and church groups. 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 $1000 from each church group and $2000 from each neighborhood organization, and she has a maximum of 16 hours of letter-writing time and a maximum of 12 hours of follow-up time available per month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month.
Set up an initial simplex tableau and use the simplex method to solve the following application problem. Please include appropriate units/explanations with your answers. Application: Liz is working to raise money for breast cancer research by sending informational letters to local neighborhood organizations and church groups. 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 $1000 from each church group and $2000 from each neighborhood organization, and she has a maximum of 16 hours of letter-writing time and a maximum of 12 hours of follow-up time available per month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month.
Initial simplex tableau:
Final simplex tableau:
Answers and interpretation:
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