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 Xi 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 4
2:00-3:00 5
3:00-4:00 10
4:00-5:00 4
5:00-6:00 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 qi 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)
Answer: d