Business Analytics - EPGDM 105 - Skew Symmetric Matrix - Operations Research Mid Term Assignment Help

EPGDM 105 - Skew Symmetric Matrix - Operations Research Mid Term Assignment Help

Assignment Task:

1. Illustrate the following:
     a. Symmetric and skew-symmetric matrix
     b. Linear Dependence and Independence
     c. Eigen Values and Eigen Vectors d. Condition of Inverse and Determinant of a matrix

2. There is a marketing analysis of three products with three competitors and it has the following
   information: A purchases 4 units of Z and sells 3 units of X and 5 units of Y; B purchases 3 units of
   Y and sells 2 units of X and 1 unit Z; and C purchases 1 unit of X and sells 4 units of Y and 6 units of Z. In this process, A, B, and C earn $6000, $5000 and $13000 respectively. Using matrix algebra, find out the prices per unit of commodity.                            

3. A company makes two products (X and Y) using two machines (A and B). Each unit of X requires 50 minutes of processing time on machine A and 30 minutes processing time on machine B. Each unit of Y requires 24 minutes processing time on machine A and 33 minutes processing time on machine B. At the start of the current week there are 30 units of X and 90 units of Y in stock.
   Available processing time on machine A is forecasted to be 40 hours and on the machine, B is forecasted to be 35 hours. The demand for X in the current week is forecasted to be 75 units and for Y is forecasted to be 95 units. Company policy is to maximize the combined sum of the units of X and the units of Y in stock at the end of the week. Formulate the problem of deciding how much of each product to make in the current week as a linear program. Solve this linear program graphically.                                       

4. A carpenter makes tables and chairs. Each table can be sold for a profit of £30 and each chair for a profit of £10. The carpenter can afford to spend up to 40 hours per week working and takes six hours to make a table and three hours to make a chair. Customer demand requires that he makes at least three times as many chairs as tables. Tables take up four times as much storage space as chairs and there is room for at most four tables each week. Formulate this problem as a linear programming problem and solve it graphically.                        

5.
a. What is a standard form of Linear Programming Problem? What is the condition of moving from Graphical method of solution of LP to Simplex method?
b. Write down the assumptions of a linear programming problem and explain in brief.
c. What is the significance of finding the dual of a primal linear programming problem?
d. Explain the difference between primal simplex and dual simplex method.
e. What is the condition of getting an alternative solution and infeasible solution in – (i) primal simplex, (ii) dual simplex?            

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