Chapter 4.2, Problem 45E

Management A bank has two types of branches. A satellite branch employs 3 people, requires $100,000 to construct and open, and generates an average daily revenue of $10,000. A full-service branch employs 6 people, requires $140,000 to construct and open, and generates an average daily revenue of $18,000. The bank has up to $2.98 million available to open new branches, and has decided to limit the new branches to a maximum of 25 and to hire at most 120 new employees.

(a) How many branches of each type should the bank open in order to maximize the average daily revenue? Find the maximum average daily revenue.

(b) At the optimal solution from part (a), analyze the bank’s constraints (number of new branches, number of new employees, and budget) to determine the “Amount Available,” “Amount Used,” and “Amount Not Used (Slack).”

(c) Obtaining additional quantities of which constraint items would have the potential to increase the bank’s average daily revenue? Explain.

(d) Obtaining more of which constraint item would not increase average daily revenue? Explain.