A computer manufact. company has 2 assembly plants, plant A and plant B, and two

Question

A computer manufact. company has 2 assembly plants, plant A and plant B, and two distribution outlets, outlet 1 and outlet 2. Plant A can assemble at most 850 computers a month and Plant B can assemble at most 650 computers a month. Outlet 1 must have atleast 400 computers a month and outlet 2 must have 900 a month. Transportation costs for shipping one computer from each plant to each outlet are as follows: $3 from plant A to outlet ; $4 from plant A to outlet II; $6 from plant B to outlet 1 and $5 from plant B to outlet 2. Find a shipping schedule that will minimize the total cost of shipping the computers from the assembly plants to the distribution outlets. Ship____ computers from plant A to outlet 1 ship____computers from plant A to outlet 2 ship___ computers from plant B to outlet 1 ship___ computers from plant B to outlet 2 The minimum shipping cost is ____

Explanation / Answer

a computer manufacturing company has two assembly plants, plant A and plant B, and two distribution outlets, out let I and outlet II, plant A can assemble at most 700 computers a month, and plant B can assemble at most 900 computers a month, outlet I must have at least 500 computers a month, and outlet II must have at least 1,000 computers a month, transportation costs for shipping one computer from each plant are as follows;$6 from plant A to outlet I; $5 from plant A to outlet II, $4 from plant B to outlet I; $8 from plant B to outlet II. find a shipping schedule that will minimize the total cost of shipping the computers from the assembly plants to the distribution outlets. What is the minimum cost? (Use simplex method)

How do I set this problem up? like what are the constraints and cost function? a computer manufacturing company has two assembly plants, plant A and plant B, and two distribution outlets, out let I and outlet II, plant A can assemble at most 700 computers a month, and plant B can assemble at most 900 computers a month, outlet I must have at least 500 computers a month, and outlet II must have at least 1,000 computers a month, transportation costs for shipping one computer from each plant are as follows;$6 from plant A to outlet I; $5 from plant A to outlet II, $4 from plant B to outlet I; $8 from plant B to outlet II. find a shipping schedule that will minimize the total cost of shipping the computers from the assembly plants to the distribution outlets. What is the minimum cost? (Use simplex method)

How do I set this problem up? like what are the constraints and cost function? a computer manufacturing company has two assembly plants, plant A and plant B, and two distribution outlets, out let I and outlet II, plant A can assemble at most 700 computers a month, and plant B can assemble at most 900 computers a month, outlet I must have at least 500 computers a month, and outlet II must have at least 1,000 computers a month, transportation costs for shipping one computer from each plant are as follows;$6 from plant A to outlet I; $5 from plant A to outlet II, $4 from plant B to outlet I; $8 from plant B to outlet II. find a shipping schedule that will minimize the total cost of shipping the computers from the assembly plants to the distribution outlets. What is the minimum cost? (Use simplex method)

How do I set this problem up? like what are the constraints and cost function? we have to MINIMIZE the total cost of shipping
Name
x1 = number of computers assembled in plant A and transported to outlet I
x2 = number of computers assembled in plant A and transported to outlet II
x3 = number of computers assembled in plant B and transported to outlet I
x4 = number of computers assembled in plant B and transported to outlet II
Then we have
shipping cost = 6 x1 + 5 x2 + 4 x3 + 8 x4, to be minimized
we have as constraints
x1+x2<=700
x3+x4<=900
x1+x3>=500
x2+x4>=1000
I have a simplex program that calculates maximisation problems so
i will convert this to a maximising problem :
maximise -6x1-5x2-4x3-8x4
under the constraints
x1+x2 <= 700
x3+x4 <= 900
-x1 -x3 <= -500
-x2 -x4 <= -1000

The simplex tableau's are :

0.00000 1.00000 2.00000 3.00000 4.00000 0.00000
-1.00000 1.00000 1.00000 0.00000 0.00000 700.00000
-2.00000 0.00000 0.00000 1.00000 1.00000 900.00000
-3.00000 -1.00000 0.00000 -1.00000 0.00000 -500.00000
-4.00000 0.00000 -1.00000 0.00000 -1.00000 -1000.00000
0.00000 6.00000 5.00000 4.00000 8.00000 0.00000

Pivoting around element(3,1) yields :
0.00000 -3.00000 2.00000 3.00000 4.00000 0.00000
-1.00000 1.00000 1.00000 -1.00000 0.00000 200.00000
-2.00000 0.00000 0.00000 1.00000 1.00000 900.00000
1.00000 -1.00000 -0.00000 1.00000 -0.00000 500.00000
-4.00000 0.00000 -1.00000 0.00000 -1.00000 -1000.00000
0.00000 6.00000 5.00000 -2.00000 8.00000 -3000.00000

Pivoting around element(1,2) yields :
0.00000 -3.00000 -1.00000 3.00000 4.00000 0.00000
2.00000 1.00000 1.00000 -1.00000 0.00000 200.00000
-2.00000 0.00000 -0.00000 1.00000 1.00000 900.00000
1.00000 -1.00000 0.00000 1.00000 0.00000 500.00000
-4.00000 1.00000 1.00000 -1.00000 -1.00000 -800.00000
0.00000 1.00000 -5.00000 3.00000 8.00000 -4000.00000

Pivoting around element(3,3) yields :
0.00000 -3.00000 -1.00000 1.00000 4.00000 0.00000
2.00000 0.00000 1.00000 1.00000 0.00000 700.00000
-2.00000 1.00000 -0.00000 -1.00000 1.00000 400.00000
3.00000 -1.00000 0.00000 1.00000 0.00000 500.00000
-4.00000 0.00000 1.00000 1.00000 -1.00000 -300.00000
0.00000 4.00000 -5.00000 -3.00000 8.00000 -5500.00000

Pivoting around element(4,4) yields :
0.00000 -3.00000 -1.00000 1.00000 -4.00000 0.00000
2.00000 0.00000 1.00000 1.00000 0.00000 700.00000
-2.00000 1.00000 1.00000 0.00000 1.00000 100.00000
3.00000 -1.00000 0.00000 1.00000 0.00000 500.00000
4.00000 -0.00000 -1.00000 -1.00000 -1.00000 300.00000
0.00000 4.00000 3.00000 5.00000 8.00000 -7900.00000

so the solution is

minimum cost = 7900
x1 = 0 ; x2 = 700 ; x3 = 500; x4 = 300 we have to MINIMIZE the total cost of shipping
Name
x1 = number of computers assembled in plant A and transported to outlet I
x2 = number of computers assembled in plant A and transported to outlet II
x3 = number of computers assembled in plant B and transported to outlet I
x4 = number of computers assembled in plant B and transported to outlet II
Then we have
shipping cost = 6 x1 + 5 x2 + 4 x3 + 8 x4, to be minimized
we have as constraints
x1+x2<=700
x3+x4<=900
x1+x3>=500
x2+x4>=1000
I have a simplex program that calculates maximisation problems so
i will convert this to a maximising problem :
maximise -6x1-5x2-4x3-8x4
under the constraints
x1+x2 <= 700
x3+x4 <= 900
-x1 -x3 <= -500
-x2 -x4 <= -1000

The simplex tableau's are :

0.00000 1.00000 2.00000 3.00000 4.00000 0.00000
-1.00000 1.00000 1.00000 0.00000 0.00000 700.00000
-2.00000 0.00000 0.00000 1.00000 1.00000 900.00000
-3.00000 -1.00000 0.00000 -1.00000 0.00000 -500.00000
-4.00000 0.00000 -1.00000 0.00000 -1.00000 -1000.00000
0.00000 6.00000 5.00000 4.00000 8.00000 0.00000

Pivoting around element(3,1) yields :
0.00000 -3.00000 2.00000 3.00000 4.00000 0.00000
-1.00000 1.00000 1.00000 -1.00000 0.00000 200.00000
-2.00000 0.00000 0.00000 1.00000 1.00000 900.00000
1.00000 -1.00000 -0.00000 1.00000 -0.00000 500.00000
-4.00000 0.00000 -1.00000 0.00000 -1.00000 -1000.00000
0.00000 6.00000 5.00000 -2.00000 8.00000 -3000.00000

Pivoting around element(1,2) yields :
0.00000 -3.00000 -1.00000 3.00000 4.00000 0.00000
2.00000 1.00000 1.00000 -1.00000 0.00000 200.00000
-2.00000 0.00000 -0.00000 1.00000 1.00000 900.00000
1.00000 -1.00000 0.00000 1.00000 0.00000 500.00000
-4.00000 1.00000 1.00000 -1.00000 -1.00000 -800.00000
0.00000 1.00000 -5.00000 3.00000 8.00000 -4000.00000

Pivoting around element(3,3) yields :
0.00000 -3.00000 -1.00000 1.00000 4.00000 0.00000
2.00000 0.00000 1.00000 1.00000 0.00000 700.00000
-2.00000 1.00000 -0.00000 -1.00000 1.00000 400.00000
3.00000 -1.00000 0.00000 1.00000 0.00000 500.00000
-4.00000 0.00000 1.00000 1.00000 -1.00000 -300.00000
0.00000 4.00000 -5.00000 -3.00000 8.00000 -5500.00000

Pivoting around element(4,4) yields :
0.00000 -3.00000 -1.00000 1.00000 -4.00000 0.00000
2.00000 0.00000 1.00000 1.00000 0.00000 700.00000
-2.00000 1.00000 1.00000 0.00000 1.00000 100.00000
3.00000 -1.00000 0.00000 1.00000 0.00000 500.00000
4.00000 -0.00000 -1.00000 -1.00000 -1.00000 300.00000
0.00000 4.00000 3.00000 5.00000 8.00000 -7900.00000

so the solution is

minimum cost = 7900
x1 = 0 ; x2 = 700 ; x3 = 500; x4 = 300 we have to MINIMIZE the total cost of shipping
Name
x1 = number of computers assembled in plant A and transported to outlet I
x2 = number of computers assembled in plant A and transported to outlet II
x3 = number of computers assembled in plant B and transported to outlet I
x4 = number of computers assembled in plant B and transported to outlet II
Then we have
shipping cost = 6 x1 + 5 x2 + 4 x3 + 8 x4, to be minimized
we have as constraints
x1+x2<=700
x3+x4<=900
x1+x3>=500
x2+x4>=1000
I have a simplex program that calculates maximisation problems so
i will convert this to a maximising problem :
maximise -6x1-5x2-4x3-8x4
under the constraints
x1+x2 <= 700
x3+x4 <= 900
-x1 -x3 <= -500
-x2 -x4 <= -1000

The simplex tableau's are :

0.00000 1.00000 2.00000 3.00000 4.00000 0.00000
-1.00000 1.00000 1.00000 0.00000 0.00000 700.00000
-2.00000 0.00000 0.00000 1.00000 1.00000 900.00000
-3.00000 -1.00000 0.00000 -1.00000 0.00000 -500.00000
-4.00000 0.00000 -1.00000 0.00000 -1.00000 -1000.00000
0.00000 6.00000 5.00000 4.00000 8.00000 0.00000

Pivoting around element(3,1) yields :
0.00000 -3.00000 2.00000 3.00000 4.00000 0.00000
-1.00000 1.00000 1.00000 -1.00000 0.00000 200.00000
-2.00000 0.00000 0.00000 1.00000 1.00000 900.00000
1.00000 -1.00000 -0.00000 1.00000 -0.00000 500.00000
-4.00000 0.00000 -1.00000 0.00000 -1.00000 -1000.00000
0.00000 6.00000 5.00000 -2.00000 8.00000 -3000.00000

Pivoting around element(1,2) yields :
0.00000 -3.00000 -1.00000 3.00000 4.00000 0.00000
2.00000 1.00000 1.00000 -1.00000 0.00000 200.00000
-2.00000 0.00000 -0.00000 1.00000 1.00000 900.00000
1.00000 -1.00000 0.00000 1.00000 0.00000 500.00000
-4.00000 1.00000 1.00000 -1.00000 -1.00000 -800.00000
0.00000 1.00000 -5.00000 3.00000 8.00000 -4000.00000

Pivoting around element(3,3) yields :
0.00000 -3.00000 -1.00000 1.00000 4.00000 0.00000
2.00000 0.00000 1.00000 1.00000 0.00000 700.00000
-2.00000 1.00000 -0.00000 -1.00000 1.00000 400.00000
3.00000 -1.00000 0.00000 1.00000 0.00000 500.00000
-4.00000 0.00000 1.00000 1.00000 -1.00000 -300.00000
0.00000 4.00000 -5.00000 -3.00000 8.00000 -5500.00000

Pivoting around element(4,4) yields :
0.00000 -3.00000 -1.00000 1.00000 -4.00000 0.00000
2.00000 0.00000 1.00000 1.00000 0.00000 700.00000
-2.00000 1.00000 1.00000 0.00000 1.00000 100.00000
3.00000 -1.00000 0.00000 1.00000 0.00000 500.00000
4.00000 -0.00000 -1.00000 -1.00000 -1.00000 300.00000
0.00000 4.00000 3.00000 5.00000 8.00000 -7900.00000

so the solution is

minimum cost = 7900
x1 = 0 ; x2 = 700 ; x3 = 500; x4 = 300

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