Note: This Problem Requires the Use of a Linear Programming $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if crew } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$

question 7

Multiple Choice

Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver.
The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process.
Min 200x1 + 250x2 + 225x3 + 190x4 +215x5 + 245x6 + 235x7 + 220x8
s.t. x1 + x2 + x5 + x7 ? 1 {Building A constraint}
X1 + x2 + x3 ? 1 {Building B constraint}
X6 + x8 ? 1 {Building C constraint}
X1 + x4 + x7 ? 1 {Building D constraint}
X2 + x7 ? 1 {Building E constraint}
X3 + x8 ? 1 {Building F constraint}
X2 + x5 + x7 ? 1 {Building G constraint}
X1 + x4 + x6 ? 1 {Building H constraint}
X1 + x6 + x8 ? 1{Building I constraint}
X1 + x2 + x7 ? 1 {Building J constraint} $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if crew } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$
Set up the problem in Excel and find the optimal solution. What is the cost of the optimal set of locations?

• A) 255
• B) 355
• C) 455
• D) 555
• E) 655

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Definitions:

Excess Reserves

Bank reserves exceeding the reserve requirements set by the central bank, available for lending.

Reserve Requirements

Rules established by central banks that specify the lowest reserve amount that banks are required to maintain against customer deposits.

Checking Accounts

Bank accounts on which the account holder can draw checks against the money deposited.

Time Deposits

Banking or financial accounts that hold funds for a fixed period, during which the depositor cannot access their money without incurring a penalty.