For a telephone suevey, a marketing research group neuds to contact at least $150$ people between the ages of $18$ and $25,120$ people between $26$ and $40,100$ people between $41$ and $60,$ and $110$ people over the age of $60,$ it costs $$2$ to make a daytime call and $($because of higher labor costs$)55$ to make an evening call. The following table lists the percentages of age groups reached by daytime and evening

Age of person responding

Percent of daytime calls

$18-25$

$30$

$26-40$

$10$

$41-60$

$10$

$60+$

$10$

Percent of evening calls

$30$

$30$

$15$

$20$

None

$40$

In order to minimize total cost of calls, you developed this LINGO model:

NODEL$$

SETS:

AgeGroup $/18\_25.26\_40,$ Calls $/$daytime$,$ tanswer of part ala

ENDSETS

SOplus$/$s MinRequired:

tanswer of part cl$?$

DATA:

MinRequired $-150,120,100,110?$

cost $=2,5$:

fraction $-0\mathrm{.}3$

$0\mathrm{.}1$

$0\mathrm{.}1$

$0\mathrm{.}1$

$0\mathrm{.}3$

$0\mathrm{.}3$

$0\mathrm{.}15$

$0\mathrm{.}2$:

ENDDATA

END

a$)$ Declare the missing set $(5$ pts$.)$

b$)$ Write the objective function $(5$ pts$.)$

c$)$ Write the missing constraint $(5$ pts$.)$