Consider the following Transportation problem:FactoryABCDDemand179119602511101020Godowns37669404711262055294063581240StockAvailable60209050It is not possible to transport any quantity from Factory B to Godown 5. Determine:(a) Basic Feasible Solution by Vogel's Approximation Method.(b) Optimum solution using MODI method.

Transportation problem: It is a special kind of linear programming problem in which goods are…

Answered: Consider the following Transportation…

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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Given an annual capital investment of RM x million, along with the employment of y million unskilled labour hours and z million skilled labour hours per year, the annual sugar production output (in tonnes) of a sugarcane mill can be modelled by the function 16 Q(x, y, z) = - -enz 100 in which the values of x, y, and z should adhere to the budget constraint of 2x² + y² + 2z² = 21 Apply both the D-test method AND the method of Lagrange multipliers to determine the optimal allocation of capital investment and the most effective utilization of unskilled and skilled labour force to maximize sugar production. Then, compare and comment on the two methods used.
The Sail-Sea is a boat manufacturer. The assembly location is available for production of 60 boats for 240 minutes per day. Given the information in the table, 1) Assign the tasks to workstations using the most follower method 2) What is the maximum theoretical capacity this line can achieve in 240 minutes
Suppose the labor cost (in dollars) for manufacturing a particular product can be approximated by 3 L(x, y) = 1⁄2 x² + y² − 5x − 6y − 2xy + 221 where x is the number of hours required by a skilled craftsperson and y is the number of hours required by a semiskilled person. What values of x and y will minimize cost and what is the minimum cost? Labor costs will be minimized when x = The minimum labor cost will be $ and y= =
8. A firm's total cost function is given by TC = 30 + 20,0, + 7Q; Where 9 and O denote the number of items of goods 1 and 2, respectively that are produced. Using the substitution method, find the values of 9 and O which minimize costs if the firm is committed to producing 40 goods of either type in total.
4. Regarding the labor-leisure trade off. Assume Sue Ellen Walton has the utility function U(C,L) = C^(½)L^(½). She sleeps 8 hours per day, which leaves her 16 hours to allocate between labor and leisure. Her wage is $10 per hour and has no non-labor income.Using the Lagrange multiplier method, what is the optimal amount of leisure she consumes per day? Points are only awarded if the Lagrange multiplier method is used.How many hours per day does she work? What is her level of consumption? Use a labor-leisure graph to show her optimal allocation between %3D consumption and leisure.
The table below shows the cost of transporting a unit item in the given routes; FROM/TO 1 2 3 4 SUPPLY 10 8 12 0 100 6 7 4 0 150 10 9 6 0 250 DEMAND 12080 200 100 A B a) A basic feasible solution is obtained using LCM as a11, x12, X23, 231, X33 , X34. Obtain the basic variables. T11= * 12 = 223 = 231 = T33 = 234 = b) A basic feasible solution is obtained using VAM as 11, *12, T23, X31, T 33 , X34. Obtain the basic variables. I14= 221 = 223 = T32 = 233 = c) Between the two solutions, which one has the least cost?

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