POM MTh 8:30-9:50 AM, Spring 2017 Exam 2 -In-Class Exam-Part 2 November 13th, 20

Question

POM MTh 8:30-9:50 AM, Spring 2017 Exam 2 -In-Class Exam-Part 2 November 13th, 2017 Guidelines: Answer all four questions in the books provided to you. Each problem carries 25 points. Write only the formulation. I think problem 4 is the most difficult one. Follow the main steps of formulating an LP type of problem: 1. 2. 3. Define Variables-5 points Define the Objective Function - 10 points Define the Constraints-10 points Question 1. Assignment type problem. An electronics firm produces electronic equipment, which it supplies to various electrical manufacturers Quality control records indicate that different employees produce different numbers of defective items The average number of defects produced by each employee for each of five components is given in Table 1 below: Table 1. Average Number of Defects per Employee mponent Employee A BCD 25 25 281 27 24 26 18 22 18 19 23 21 19 29 17 15 29 30 14 28 6 1828 16 16 27 17 16 Formulate the problem as an LP that will minimize the total average number of defects produced by the firm each month. Define the variables, objective function and constraints Question 2. Transshipment type problem. You are given the following transshipment problem. The supply is depicted at auto plants 1 and 2, there are two transshipment centers at nodes 3 and 4 and demand is depicted at the three dealers at nodes 5, 6, 7. As you may have noticed, the transshipment centers are connected to each other and cars can be transported from center 3 to center 4 as necessary. Also the dealerships at 5 and 7 can receive cars from dealer 6. The transfer center 3 has a capacity of 1500 autos. The transfer center 4 has a capacity of 1600 autos. The corresponding travel costs are depicted at each roadway link in Figure 1 below: a) 20 points Formulate the problem as an LP b) 5 points - Assume that the auto plant one (1) has increased its capability to produce an additional 100 autos to a total of 1500 autos. Show the change in the constraints because of this extra capability of auto plant 1.

Explanation / Answer

Answer of Question 1)

Given that, Table of Average number of defects of 5 components per employee.

let, there is 6 variables corresponding to 6 employee as,

X1: total average number of defects produces by employee 1 by firm for each month.

X2:total average number of defects produces by employee 2 by firm for each month.

X3: total average number of defects produces by employee 3 by firm for each month.

X4: total average number of defects produces by employee 4 by firm for each month.

X5: total average number of defects produces by employee 5 by firm for each month.

and

X6: total average number of defects produces by employee 6 by firm for each month.

let, objective function is as

Min Z= X1+X2+X3+X4+X5+X6

Such That, Constraints are as

For Component 1(A): 25*X1+27*X2+24*X3+18*X4+22*X5+19*X6 >= 1

For Component 2(B): 25*X1+17*X2+26*X3+17*X4+18*X5+23*X6 >= 1

For Component 3(C): 28*X1+15*X2+30*X3+16*X4+16*X5+21*X6 >=1

For Component 4(D): 14*X1+29*X2+14*X3+18*X4+16*X5+19*X6 >=1

For Component 5(E): 11*X1+14*X2+28*X3+28*X4+27*X5+29*X6 >=1

And, non-negativity restrication is as

X1, X2, X3, X4, X5 and X6 > 0(zero)

For Question 2, There is insufficient information. They do not give a table of travel cost.

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