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G1159 Pages: 2

The ABC company has been a producer of picture tubes for television sets and
certain printed circuits for radios. The company has just expanded into full scale
production and marketing of AM and AM-FM radios. It has built a new plant
that can operate 48 hours per week. Production of an AM radio in the new plant
will require 2 hours and production of an AM-FM radio will require 3 hours.
Each AM radio will contribute Rs. 40 to profits while an AM-FM radio will
contribute Rs. 80 to profits. The marketing department after extensive research
has determined that a maximum of 15 AM radios and 10 AM-FM radios can be
sold each week

i. Formulate a linear programming model to determine the optimal

production mix of AM-FM radios that will maximise profits.
ii. Solve the problem by simplex method.

PART C

Answer any two full questions, each carries 20 marks.
Find y(0.1), 2(0.1) from the system of equations y’ = x+z മ്‌ = x-y” given y(0) =
2, 2(0) = 1 using Runge Kutta Method of fourth order
Use Tailor series method solve y’= വ്‌, y(0) = 0 for (0, 0.4) using two
subintervals of size 0.2
Solve the equation y’’ =x + ۲ with boundary conditions y(0) = y(1) = 0.
Use Bender Schmidt explicit method to solve प्रा = uxx under the conditions u(0,t)
= u(1,t) = 0 and u (x,0) = sin mx , 0
List 5 techniques of unconstrained optimisation.

− −∑−∑
Maximise the function f 0 y) = 2xy + 2x —x*—2y with initial guesses x = -

1 and y = | using steepest descent method.

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