Question

Need optimal solution for x,y, and value Z

The Attaran Corporation manufactures two electrical products: portable air conditioners and portable heaters. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each heater must go through 2 hours of wiring and 1 hour of drilling During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each heater assembled may be sold for a $13 profit The aim of the objective function for Attaran Corporation should be to Maximize the objective value Decision variables: X number of air conditioners to be produced Y-number of heaters to be produced Objective function: Z- 25 + 13 Y 200 5080 100 120 140 160 180 200 Subject to 3x + 2Y 2X + 18 240 (C) 140 (C) S On the graph on right, constraints C, and have been drawn. Using the point drawing tool, plot all the corner points for the feasible area The optimum solution is X= (round your responso to two decimal places).

Answer 1

From the given data, the LP model becomes:- • The aim is to maximize objective value That is profet → Max 2= 25x+BY where X: no of air conditioner Y no of heaks st:- 0 3x+24 & 240 (wiring time) 2x + 4 = 140 (drilling time) X,Yzo Sowing graphically: 3x+24 240 2x+y = 140 xo 80 X o 70 4 120 o 4 140 o Teasible region is found. The points are: A = (0,120) B = (40,60) { Sowing r@ 3 c (200) Substituting in 2:- A- 2=0+13(120) = 1560 B + 2 > 25(40) + 3(60) = 1780 ( 2 > 25(70) = 1750 - Optimal solection at B. 20 40 60 80 100 120 140 » K 2 O 4 = a 2 + 78o