Deterministic Operations Research Homework Answers

In: Business and Management

Submitted By damlatulek
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MIS 208 SPRING 2015
HOMEWORK 1
(due 13:15 on Monday, 6 April 2015, in class at 101)
Reading Assignment: Please read section Duality and Sensitivity Analysis of the text book
Winston. You will be responsible on that section in the exam.
Question 1: Two different products, P1 and P2 can be manufactured by one or both of two different machines, M1 and M2. The unit processing time of either product on either machine is the same.
The daily capacity of machine M1 is 200 units (of either P1 or P2, or a mixture of both) and the daily capacity of machine M2 is 250 units. The shop supervisor wants to balance the production schedule of the two machines such that the total number of units produced on one machine is within
5 units of the number produced on the other. The profit per unit of P1 is $10 and that P2 is $15. Set up the problem as an LP in equation form.

Question 2: A company manufactures purses, shaving bags and backpacks. The construction includes leather and synthetics, leather being the scarce raw material. The production process requires two types of skilled labor: sewing and finishing. The following table gives the availability of the resources, their usage by the three products, and the profits per unit.

a) Formulate the problem as a linear program and find the optimal solution by using appropriate
Simplex Methods that you have seen in the class
b) From the optimum solution determine the status of each resource.

Question 3: The following tableau represents a specific simplex iteration. All variables are nonnegative. The tableau is not optimal for either a maximization or a minimization problem. Thus, when a non-basic variable enters the solution it can either increase or decrease z or leave it unchanged, depending on the parameters of the entering non-basic variable. 

(a) Categorize the variables as basic and non-basic and…...

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