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Solve the following problem by simplex method and check for alternative solution. If possible,
find the alternative solution also. Does this problem has infinite number of solutions ?
Maximize Z = 4x1 + 10x2
Subject to
2x1 + x2 ≤ 10
2x1+ 5x2 ≤ 20
2x1 + 3x2 ≤ 18
where x1, x2 are unrestricted in sign.
Consider the following LPP
Maximize Z = 2x1 + 3x2
Subject to
x1 + 3x2 ≤ 6
3x1 + 2x2 ≤ 6
x1, x2 ≥ 0
a. Determine all the basic solutions of the problem, and classify them as feasible and
infeasible.
b. Carry out the full tableau implementation of the simplex method, starting with the basic
feasible solution (x1, x2) = (0, 0)
Consider the set of equations
5x1 − 4x2 + 3x3 + x4 = 3
2x1 + x2 + 5x3 − 3x4 = 0
x1 + 6x2 − 4x3 + 2x4 = 15
where x1 = 1, x2 = 2, x3 = 1, x4 = 3 is a feasible solution. Is this solution feasible solution
If not, reduce this feasible solution to two different basic feasible solution.
2. A manufacturer produces two models of a certain product: model A and model B. There is a R20 profit on model A and an R35 profit on model B. Three machines M1,M2 and M3 are used jointly to manufacture these models. The number of hours that each machine operates to produce 1 unit of each model is given in the table: Model A Model B Machine M1 1 1 2 1 Machine M2 3 4 1 1 2 Machine M3 1 1 3 1 1 3 No machine is in operation more than 12 hours per day. Now let x be the number of model A made per day and y be the be the number of model B made per day. Then x and y satisfies the following constrains
A transportation problem involves the following costs, supply, and demand.
To
From 1 2 3 4 Supply
1 $500 750 300 450 12
2 650 800 400 600 17
3 400 700 500 550 11
Demand 10 10 10 10
Required:
i. Find the initial solution using the northwest corner method, the minimum cell cost
method, and Vogel's Approximation Method. Compute total cost for each.
ii. Using the VAM initial solution, find the optimal solution using the modified distribution
method (MODI).
1. A transportation problem involves the following costs, supply, and demand.
To
From
1
2
3
4
Supply
1
$500
750
300
450
12
2
650
800
400
600
17
3
400
700
500
550
11
Demand
10
10
10
10
Required:
i. Find the initial solution using the northwest corner method, the minimum cell cost method, and Vogel's Approximation Method. Compute total cost for each.
ii. Using the VAM initial solution, find the optimal solution using the modified distribution method (MODI).
1. A company produces two types of products say type A and type B. Product A is of superior quality and product B is of a lower quality. Respective profits for the two types of products are BIRR 40 and BIRR 30.
The data on the resource required, availability of resources are given below:
Requirement
Capacity available per month
Product A
Product B
Raw materials (kg)
120
60
12000
Machining time (hrs/piece)
5
8
600
Assembly (man-hour)
4
3
500
Required:
i. Formulate the problem as LPP?
ii. Solve using Simplex method.
Hint:Solve the below formulated LPM using Graphics method.
Z-Min = 1500x+2400y
Subjected to:
4x+Y>24
2x+3y>42
X+4y>36
X<14
Y<14
X, y>0 Required: Perform the below requirements by Using the Graphics method through considering
appropriate steps and procedures.
i. Solve using Graphics method?
Hint:Solve the below formulated LPM using Graphics method.
Z-Min = 1500x+2400y
Subjected to:
4x+Y>24
2x+3y>42
X+4y>36
X<14
Y<14
X, y>0 Required: Perform the below requirements by Using the Graphics method through considering
appropriate steps and procedures.
i. Solve using Graphics method?
John sells notebooks and pencils and notebooks. In a week he can sell between 400 and 500 pencils and between 150 and 200 notebooks but not more than 650 items altogether. Each pencil costs P18 and sells for P25 while each notebook costs P28 and sells for P45. How many of each type should he get to gain the maximum profit per week? 1. Formulate the problem above as a linear programming problem with objective function and constraints . Start by defining the decision variables and the profit function
#339914 on Dec 2023