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 $100 from each church group and $250 from each neighborhood group, and she has a maximum of 20 hours of letter-writing time and a maximum of 16 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 x, represent the numbers of church groups and neighborhood groups, respectively, and let z be the total amount of money raised. Maximize z 100x, + 250x2 2x, +2x, s 20 X, + 3x s 16 X1 20, x2 20. subject to (Do not factor. Do not include the $ symbol in your answers.) Liz can raise at mont $ in a month. To raise that amount, she should contact church group(s) and neighborhood group(s). (Type whole numbers.)
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 $100 from each church group and $250 from each neighborhood group, and she has a maximum of 20 hours of letter-writing time and a maximum of 16 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 x, represent the numbers of church groups and neighborhood groups, respectively, and let z be the total amount of money raised. Maximize z 100x, + 250x2 2x, +2x, s 20 X, + 3x s 16 X1 20, x2 20. subject to (Do not factor. Do not include the $ symbol in your answers.) Liz can raise at mont $ in a month. To raise that amount, she should contact church group(s) and neighborhood group(s). (Type whole numbers.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 $100 from each church group and $250 from each neighborhood group, and she has a maximum of 20 hours of
letter-writing time and a maximum of 16 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 x, represent the numbers of church groups and neighborhood groups, respectively, and let z be the total amount of money raised.
Maximize
z= 100x, + 250x2
2x, +2x, s 20
X, + 3x s 16
X1 20, x2 20.
subject to
(Do not factor. Do not include the $ symbol in your answers.)
Liz can raise at most S
(Type whole numbers.)
in a month. To raise that amount, she should contact church group(s) and neighborhood group(s).
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