Q.1 (a) Discuss Linear Programming its importance, utility along with its elements. (5) (b) Four products are processed successively on two machines. The manufacturing times in hours per unit of each product are tabulated below for the two machines. Machine 1 2 Product 1 2 3 Time per Unit (hours) Product 2 3 2 Product 3 4 1 Product 4 2 2 The total cost of producing 1 unit of each product is based directly on the machine time. Assume that the cost per hour for machine 1 and 2 is $10 and $15, respectively. The total hours budgeted for all the products on machines 1 and 2 are 500 and 380. If the sales price per unit for products 1, 2, 3 and 4 are $65, $70, $55 and $45, formulate the problem as a linear programming model to maximize the net profit. (04) 2.2 (a) Discuss standard form and its importance for solving a linear programming problem. (04) (b) Solve the following linear programming problem graphically. (04) max z = 8x2 + 5x2 Subject to x S 150, xz 0 2.3 (a) illustrate the usefulness of Two Phase method in solving linear programming problem. (04) (b) Solve the following problem by using M-technique. max 2 = x1 + x2 Subject to 2x2 + 3x2 =5, 7x + 2x, S6, X1, X2 20 (04) (8) 2.4 Write notes on the following. (i) Useful ness of Linear Programming. (ii) Importance of Feasible Region. (iii) Role of Stack variable. (iv) Elements of Linear Programming. Good Luck Q.1 (a) Discuss Linear Programming its importance, utility along with its elements. (5) (b) Four products are processed successively on two machines. The manufacturing times in hours per unit of each product are tabulated below for the two machines. Machine 1 2 Product 1 2 3 Time per Unit (hours) Product 2 3 2 Product 3 4 1 Product 4 2 2 The total cost of producing 1 unit of each product is based directly on the machine time. Assume that the cost per hour for machine 1 and 2 is $10 and $15, respectively. The total hours budgeted for all the products on machines 1 and 2 are 500 and 380. If the sales price per unit for products 1, 2, 3 and 4 are $65, $70, $55 and $45, formulate the problem as a linear programming model to maximize the net profit. (04) 2.2 (a) Discuss standard form and its importance for solving a linear programming problem. (04) (b) Solve the following linear programming problem graphically. (04) max z = 8x2 + 5x2 Subject to x S 150, xz 0 2.3 (a) illustrate the usefulness of Two Phase method in solving linear programming problem. (04) (b) Solve the following problem by using M-technique. max 2 = x1 + x2 Subject to 2x2 + 3x2 =5, 7x + 2x, S6, X1, X2 20 (04) (8) 2.4 Write notes on the following. (i) Useful ness of Linear Programming. (ii) Importance of Feasible Region. (iii) Role of Stack variable. (iv) Elements of Linear Programming. Good Luck