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Exam 3: Linear Programming Modeling Applications with Computer Analyses in Excel

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Question 31

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Use this information to answer the following questions. The following table contains information on the cost to run four jobs (1,2,3,and 4)on four available machines (A,B,C,and D). -Refer to the table above.Assume that job number 4 was canceled and will no longer be processed.How will this affect the job-machine assignment? Use Excel to model and solve this problem to determine the least costly assignment.

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Question 32

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In a multi-period production scheduling application,the decision choices in later periods are directly dependent on the decision made in earlier periods.

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Question 33

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Consider the following constraint: X₂ ≤ 30.This implies that at least 30 units of product X₂ can be produced.

A factory operates 7 days a week.Due to labor union regulations,employees are allowed to work a maximum of 5 consecutive days.The minimum number of employees that are needed on a given day is provided as follows: $\begin{array} { l c } \text { Day } & \text { Number of Employees Needed } \\\hline \text { Sunday } & 20 \\\text { Monday } & 30 \\\text { Tuesday } & 35 \\\text { Wednesday } & 40 \\\text { Thursday } & 37 \\\text { Friday } & 30 \\\text { Saturday } & 25\end{array}$ Use Excel to formulate and solve this labor planning problem to determine the minimum number of employees needed each day.

An insurance company has three secretaries,A,B,and C,who are each capable of processing four different types of insurance claims.The amount of time required by each secretary to process a particular type of a claim is summarized in the following table. On a typical week,the insurance firm has 5 type 1 claims,4 type 2 claims,2 type 3 claims,and 3 type 4 claims.Each secretary works a maximum of 40 hours per week.The office manager wants to know how many of each type of an insurance claim should be processed by each secretary to minimize the total processing time.Use Excel to formulate and solve this problem.

In a "Portfolio Selection" application,the objective function is always to minimize risk,given a set of legal and policy constraints.

An investment company currently has 1 million dollars available for investment in five different stocks.The company wants to maximize the interest earned over the next year.The five investment possibilities along with the expected interest earned are shown below.To manage risk,the investment firm wishes to have at least 35% of the investment in stocks A and B.Furthermore,no more than 15% of the investment may be in stock E.Model and solve this problem in Excel. $\begin{array} { l c } \text { Investment } & \text { Expected Interest Earned (\%) } \\ \text { Stock A } & 7 \\\text { Stock B } & 9 \\\text { Stock C } & 8 \\\text { Stock D } & 10 \\\text { Stock E } & 11\end{array}$

The objective of transportation problems is typically to either minimize total shipping costs or distances.

The "Diet" problem can be classified as an "ingredient blending" linear programming application.