A bank has two types of branches. A satellite branch employs 3 people, requires $400,000 to construct and open, and generates an average daily revenue of $10,000. A full-service branch employs 6 people, requires $560,000 to construct and open, and generates an average daily revenue of $18,000. The bank has up to $11.92 million available to open new branches and has decided to limit the new branches to a maximum of 25 and to hire at most 120 new employees. (a) How many branches of each type should the bank open to maximize the average daily revenue? Find the maximum average daily revenue. satellite branches full-service branches maximum revenue$ (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)." branchespossibleusednot usedemployeespossibleusednot usedbudgetpossible$ millionused$ millionnot used$ million
A bank has two types of branches. A satellite branch employs 3 people, requires $400,000 to construct and open, and generates an average daily revenue of $10,000. A full-service branch employs 6 people, requires $560,000 to construct and open, and generates an average daily revenue of $18,000. The bank has up to $11.92 million available to open new branches and has decided to limit the new branches to a maximum of 25 and to hire at most 120 new employees. (a) How many branches of each type should the bank open to maximize the average daily revenue? Find the maximum average daily revenue. satellite branches full-service branches maximum revenue$ (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)." branchespossibleusednot usedemployeespossibleusednot usedbudgetpossible$ millionused$ millionnot used$ million
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...
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A bank has two types of branches. A satellite branch employs 3 people, requires $400,000 to construct and open, and generates an average daily revenue of $10,000. A full-service branch employs 6 people, requires $560,000 to construct and open, and generates an average daily revenue of $18,000. The bank has up to $11.92 million available to open new branches and has decided to limit the new branches to a maximum of 25 and to hire at most 120 new employees.
(a)
How many branches of each type should the bank open to maximize the average daily revenue? Find the maximum average daily revenue.
satellite branches full-service branches maximum revenue$
(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)."
branchespossibleusednot usedemployeespossibleusednot usedbudgetpossible$ millionused$ millionnot used$ million
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