Uhura Enterprises Provides Consulting Services for Customers

Multiple Choice

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 leaves. 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 4
2:00-3:00 5
3:00-4:00 10
4:00-5:00 4
5:00-6:00 8
Suppose that if consultants start shifts at both 1:00 and 2:00, then the firm will incur an additional fixed cost of $100 (for secretarial support) . Let Y be a binary (0-1) variable that equals 1 if this event occurs, and 0 otherwise. Which of the following would "activate" Y variables.)

A) X₁ + X₂ ? 5000Y
B) X₁ ? 5000Y and X₂ ? 5000Y
C) X₁ + X₂ ? 5000Y
D) X₁ + X₂ ? Y
E) X₁ ? 5000q₁ and X₂ ? 5000q₂ and q₁ + q₂ ? 1 + Y