1 answer

Question General Ford produces cars at Malatya and Antalya and has a warehouse in Eskisehir; the...

Question:

Question General Ford produces cars at Malatya and Antalya and has a warehouse in Eskisehir; the company supplies cars to cus
b) Formulate it as a balanced transportation problem, use the northwest corner method to find a bfs.
Question General Ford produces cars at Malatya and Antalya and has a warehouse in Eskisehir; the company supplies cars to customers in Ankara and Istanbul. The cost of shipping a car between points is given in the table below. (6-" means that a shipment is not allowed). Malatya can produce as many as 1,300 cars, and Antalya can produce as many as 1,900 cars. Ankara must receive 1,400 cars, and Istanbul must receive 1,700 cars. Malatya 0 Antalya Istanbul Ankara 90 To ($) Eskisehir 100 121 0 0 From Malatya Antalya Eskisehir Ankara Istanbul 110 139 78 113 0 0 The company wishes to minimize the shipping costs incurred in meeting demands at Houston and Tampa a) Formulate the problem as an LP.
b) Formulate it as a balanced transportation problem, use the northwest corner method to find a bfs.

Answers

a)

LP is following:

Let Xij = number of cars to be shipped from location i to j, where i,j = {1,2,3,4,5} for {Malatya,Antalya,Eskisehir,Ankara,Istanbul}

Min 100X13+90X14+121X23+110X24+139X25+113X34+78X35

s.t.

X13+X14 <= 1300

X23+X24+X25 <= 1900

X13+X23-X34-X35 = 0

X14+X24+X34 = 1400

X25+X35 = 1700

Xij >= 0

--------------------------------------------------

b)

Balanced transportation problem is formulated as below:

Cost from/to Eskisehir Ankara Istanbul Dummy Capacity
Malatya 100 90 1000 0 1300
Antalya 121 110 139 0 1900
Eskisehir 0 113 78 0 3100
Demand 3100 1400 1700 100

Shipping cost of Malatya to Istanbul is written as 1000, which is hypothetically large to prohibit allocation to this cell, as shipment from Malatya to Istanbul is not allowed.

Total capacity (1300+1900=3200) is more than total demand (1400+1700=3100) . Therefore, a dummy demand node is created for balance 100 cars with shipping cost of 0.

Total demand and capacity of warehouse in Eskisehir is equal to total demand, i.e. 3100 cars

Basic Feasible Solution (bfs) is determined by northwest corner (NWC) method as follows:

In NWC method, we start with the Northwest Corner cell and allocate the maximum quantity possible and then move on to either the next cell to the right or below, depending upon the remaining demand or supply in that particular row or column. The process is repeated until all the demand is satisfied.

Resulting tableau showing the shipping quantity from each plant to warehouse to customers is following:

Eskisehir Ankara Istanbul Dummy Capacity
Malatya 1300 0 0 0 1300
Antalya 1800 100 0 0 1900
Eskisehir 0 1300 1700 100 3100
Demand 3100 1400 1700 100

Total cost = 1300*100+1800*121+100*110+1300*113+1700*78+100*0

= $ 638,300

.

Similar Solved Questions

1 answer
A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is #(5pi)/8# and the angle between B and C is # (pi)/12#. What is the area of the triangle?
A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is #(5pi)/8# and the angle between B and C is # (pi)/12#. What is the area of the triangle?...
1 answer
8) Find the output of an LTI system with the input x(t) with the sampling frequency...
8) Find the output of an LTI system with the input x(t) with the sampling frequency of fn = 10 Hz, and the filter/transfer function (el) below. x(t) = 2 + cos (2007t + ) + 2sin(1007t) Hew) = 1 + 2e1W + cos(2w)...
1 answer
Can anyone explain why covalent bonds are formed when nonmetals from the right side of the periodic table bond with each other with some examples
Can anyone explain why covalent bonds are formed when nonmetals from the right side of the periodic table bond with each other with some examples?...
1 answer
Let A and B be events with probabilities not equal to 0 or 1. Show that...
Let A and B be events with probabilities not equal to 0 or 1. Show that if P(B|A) = 1, then P(A0 |B0 ) = 1. You may use the axioms of probability, all the theorems from the notes, and anything that was proven on the homework or in the notes. Hint: Consider slide 9 in chapter 4 for event A and show t...
1 answer
PLEASE HELPPPP Customers call the Pizza Palace to order pizzas. Employees ask for the calling customer’s...
PLEASE HELPPPP Customers call the Pizza Palace to order pizzas. Employees ask for the calling customer’s phone number. If the number is recognized by the system, the customer’s profile is identified and customers proceed to order. If the number isn’t recognized, the employee asks f...
1 answer
61. (14.8) Find the extreme values for the function 8y - 4x subject to the constraints...
61. (14.8) Find the extreme values for the function 8y - 4x subject to the constraints y2 + x2 – 1 = 0 and 2x – 2 - Y - 2 = 0....
1 answer
2. value: 7.69 points Stone Company produces carrying cases for CDs it has compited the folowing...
2. value: 7.69 points Stone Company produces carrying cases for CDs it has compited the folowing information for the month of June: Physical Percent Complete for 68 00ongsrson Units Beginning work in process Ending work in process versi 55% 0l 91,000 Stone adds all materials at the beginning of its ...
1 answer
After a can of carbonated soft drink is removed from the refrigerator, opened and left to...
After a can of carbonated soft drink is removed from the refrigerator, opened and left to stand awhile. which of the following best describes the charges that cause the soda to "go flat" (i.e. lose its CO2 content)?...
1 answer
Help the high school student pleasee
find a vector function that represents the curve ofintersection of the two surfaces.the cylinder x^2+y^2=4 and the furface z=xy...
1 answer
4. (a) (10%) A player has three information sets in the game tree. He has four...
4. (a) (10%) A player has three information sets in the game tree. He has four choices in his first information set, four in his second and three in his third. How many strategies does he have in the strategic form? Circle one: (i) 11, (ii) 28 (iii) 48 (iv) 18. (b) (10%) Is it true that the followin...
1 answer
Suppose that y varies directly with x, and y= 10 when x-5 (a) Write a direct...
Suppose that y varies directly with x, and y= 10 when x-5 (a) Write a direct variation equation that relates x andy Equation: (b) Find y when x = 4 ....
1 answer
Please explain what proof and why
please explain what proof and why...
1 answer
Do you agree or disagree with the following: Electronic health records improve workflow processes. Electronic health...
Do you agree or disagree with the following: Electronic health records improve workflow processes. Electronic health records reduce costs. Please support your responses with a reference....
1 answer
COULD YOU please help me with the forth blank, and actually, I am cofused with market...
COULD YOU please help me with the forth blank, and actually, I am cofused with market recovery value, and the last two blanks, why the answer is M and N seprately. Create a cash flow diagram for the following scenario by entering the letter denoting the correct location of the corresponding paramet...