Speedy Delivery, a new mail service firm, rents docking and unloading bays from its friendly competitor at a cost of $\$ 200$ per hour, which includes the cost of unloading the crew. Each bay can unload at a rate of 2 trucks per hour. Trucks arrive at its facility at the rate of 4 per hour, and the trucking company charges $\$ 300$ per hour of time spent by the truck in the system. The arrivals are Poisson, and service is exponential. At present the firm rents 3 bays. From appropriate table, $\mathrm{L}_{\mathrm{q}}$ was found to be 0.45 . The total hourly cost of bay and truck unloading and waiting cost will be

Question

Quizplus · Accepted Answer

The total cost includes the cost of renting bays and the cost of trucks waiting. With 3 bays, the service rate is 6 trucks per hour. The cost of renting 3 bays is $3 \times 200 = \$ 600$. The average number of trucks waiting in the queue is $\mathrm{L}_{\mathrm{q}} = 0.45$, and the cost per truck waiting is $\$ 300$. Therefore, the waiting cost is $0.45 \times 300 = \$ 135$. The total cost is $600 + 135 = \$ 735$.

Speedy Delivery, a New Mail Service Firm, Rents Docking and Unloading