Answer Happy

Garden City Beach is a popular summer vacation destination for
thousands of people. Each summer, the city hires temporary
lifeguards to ensure the safety of the vacationing public. Garden
City's lifeguards are assigned to work five consecutive days each
week and then have two days off. However, the city's insurance
company requires them to have at least the following number of
lifeguards on duty each day of the week. Minimum Number of
Lifeguards Required Each Day Sunday 18 Monday 17 Tuesday 16
Wednesday 16 Thursday 16 Friday 15 Saturday 20
The city manager would like to determine the minimum number of
lifeguards that will have to be hired.
(a)
Formulate an ILP for this problem.
(Let X1 be the number of lifeguards
whose shift starts on Sunday, X2 be
the number of lifeguards whose shift starts on Monday, …,
and X7 be the number of lifeguards
whose shift starts on Saturday.)
MIN:
Subject to:Sunday constraint
Monday constraint
Tuesday constraint
Wednesday constraint
Thursday constraint
Friday constraint
Saturday constraint
all Xi ≥ 0
all Xi must be integers
(b)
Implement your model in a spreadsheet and solve it. What is the
optimal solution?
(X1, X2, X3, X4, X5, X6, X7)
=