1. Use the minimum-entry and u-v methods to solve the following balanced minimum-cost trans-portation problem:W₁W₂W3DemandsM₁1M2 M3 M4 Supplies2266104543301696208 102022Use Bland's rule to choose entering and leaving variables where variables/cells are ordered from topto bottom and left to right.

SuppliesM4M3M2M122 6 6 10W₁5 4 3 30W2 4W3 16 9 6 20Demands 8102022Use Bland's rule to choose…

Answered: 1. Use the minimum-entry and u-v…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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7 You are given the following Cobb-Douglas utility function: u(x, y) = Axªy¹ and the budget constraint px +qy=m. (A, a, b, p, q, m > 0) a. Solve the following maximization problem using the Lagrange multiplier method: max Axay st. px + qy = m b. Give an interpretation of the Lagrange multiplier A. c.Show that the demand functions are homogeneous of degree zero.
A function, z = ax + by, is to be optimized subject to the constraint, x2 + y2=1 where a and b are positive constants. Use Lagrange multipliers to show that this problem has only one solution in the positive quadrant (i.e. in the region x > 0, y > 0) and that the optimal value of z is √a2 +b2.
A manufacturing firm will deliver its finished goods from three factories to three different warehouses as follows. Determine the total cost of transportation using Column Minima Method, and Vogel's Approximation Method. F1 F2 F3 Warehouse Requirement W1 10 9 12 35 W2 13 10 8 20 W3 14 8 15 25 Factory Capacity 25 25 30
7. A consumer’s utility function is given by U=2*x*y+3*x where x and y denote the number of items of two goods (good 1 and good 2) that are bought. Each item costs €1 for good 1 and €2 for good 2. The consumer’s budget per day is €95, which is x+2y=95. If we use the Lagrange multiplier method to maximize the level of utility per day subject to that constraint. Find the values of “x” and “y” which maximize the level of utility subject to that constraint.
(plss solve it due to 18.00) Question 1: Four units of X, three units of Y and two units of Z need to be produced. X uses one unit of A and two units of B, Y uses two units of A and one unit of B and Z uses two units of A and three units of B. Use Monden's heuristic to determine the sequence of end products to be processed such that the demand variation for the components is minimized.
Answer question 9 only
1. The manager of an oil refinery must decide on the optimal mix of two possible blending processes of which the inputs and output per production run are as follows: Process 1. 2. Input (Units) Crude A 5 4 Crude B 3 5 Output (Units) Gasoline X 5 4 Gasoline Y 8 4 The maximum amount available for crude A and B is 200 units and 150 units respectively. Market requirement show that at least 100 units of gasoline X and so units of gasoline Y must be produced. The profits per production run from process 1 and process 2 are Rs. 300 and Rs. 400 respectively. Solve the L.P. by simple method.
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y, z) = x² + y² + z²; x4 + yA + zA = 5 %3D maximum value minimum value
2.2. You are provided with the following Hessian matrix from a constrained optimisation prob- lem: 1 2.x 1 1 1 2x 1 2x For which values of x: (a) will the solution be a local constrained maximum? (b) will the solution be a strict local constrained maximum? (c) will the solution be a strict local constrained minimum?
II. Consider the transportation problem having the following parameter table: Destination 2 3 5 Supply 5 1 4 1 13 10 22 29 18 2 14 13 16 21 M 3 3 M 11 7 4 18 19 23 11 4 5 30 24 34 36 28 Demand 3 5 4 5 6 Use each of the following criteria to obtain an initial BF solution. Compare the values of the objective function for these solutions. (a) Northwest corner rule. (b)Least cost Method Source

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