Uhura Enterprises provides consulting services for customers. Consultants are brought in for two-hour shifts. A consultant will spend one full hour with a customer. The customers remain for that hour and then leave. Each consultant is paid $25 per hour. Let X_i represent the number of consultants starting their shift at hour i, (i = 1,2,3,4). The firm wishes to minimize salary costs while satisfying demand. Customer demand is as follows.
1:00-2:00

\quad

4
2:00-3:00

\quad

5
3:00-4:00

\quad

10
4:00-5:00

\quad

4
5:00-6:00

\quad

8
Suppose that two of the customers scheduled to arrive at 1:00 could be rescheduled to arrive at 2:00. Which of the following sets of constraints would allow for this rescheduling option? (In the options below, q and q_i are binary (0-1)variables.)
A)X₁ ≥ 4 and X₂ ≥ 5 and X₁ ≥ 2 and X₂ ≥ 7
B)X₁ ≥ 4 and X₂ + X₃ ≥ 15 and X₁ ≥ 2 and X₂ + X₃ ≥ 17
C)50X₁ ≥ 4 and 50X₂ + 50X₃ ≥ 15 and 50X₁ ≥ 2 and 50X₂ + 50X₃ ≥ 17
D)X₁ ≥ 4 - 5000q and X₂ + X₃ ≥ 15 - 5000q and X₁ ≥ 2 -5000(1-q)and X₂ + X₃ ≥ 17 -5000(1-q)
E)X₁ ≥ 4 + 5000q and X₂ + X₃ ≥ 15 + 5000q and X₁ ≥ 2 + 5000(1-q) and X₂ + X₃ ≥ 17 + 5000(1-q)

Consider the Following Three Functions

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