A company makes three types of widgets. Type 1 widget requires 10 lbs. of essence of...
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A company makes three types of widgets. Type 1 widget requires 10 lbs. of essence of widget to produce while types 2 and 3 require 10 and 20 lbs., respectively. Type 1 and type 3 widgets are also put through a widget enhancement process to increase their value. This requires 2 hours for a batch of 100 type 1 widgets and 3 hours for a batch of 100 type 3 widgets. There are only 5 hours of enhancement processing available per day. The total number of daily production hours, excluding the widget enhancement time, is limited to 7. The widgets take 2, 1, and 3 hours to produce 100 widget batches of the type 1, type 2, and type 3 widgets, respectively. If there are only 4000 lbs. of essence of widget available per day and the per widget profits are $3, $2, and $4 for types 1, 2, and 3 widgets, respectively, then what is the daily production schedule that maximizes profit? The plant manager has formulated this problem as an LP with initial tableau X3 X4 X5 16 | 1 (essence of widget) (enhancement time) .02 (production time) 10 10 20 0 | 4000 0.03 1 .02 .01 .03 1 | 7 3 4 0. The associated optimal tableau is x3 X4 X5 X6 | (essence of widget) (enhancement time) (production time) 1 .5 .1 -50 150 1 1.5 250 0 -.005 -.001 -.5 1 .5 -1.5 -2 -50 -1050 (a) (15 points) What is the range of the widget enhancement time resource that preserves the currently optimal basis as optimal? (b) (10 points) By how much does this production process increase the value of each hour of widget enhancement time? (c) (10 points) If you could purchase more widget enhancement time, how much more would you be willing to pay for it than you are currently paying, and how many hours should you purchase? (d) (15 points) Do not consider questions (a)-(c) above in answering this question. Due to illness, we expect to loose one hour each of widget enhancement time and widget production time for the next few days. Use the techniques of sensitivity analysis to determine the new production schedule during this time. Hint: The perturbed right-hand side takes the form b+ Ab where Ab = -[0, 1, 1]". A company makes three types of widgets. Type 1 widget requires 10 lbs. of essence of widget to produce while types 2 and 3 require 10 and 20 lbs., respectively. Type 1 and type 3 widgets are also put through a widget enhancement process to increase their value. This requires 2 hours for a batch of 100 type 1 widgets and 3 hours for a batch of 100 type 3 widgets. There are only 5 hours of enhancement processing available per day. The total number of daily production hours, excluding the widget enhancement time, is limited to 7. The widgets take 2, 1, and 3 hours to produce 100 widget batches of the type 1, type 2, and type 3 widgets, respectively. If there are only 4000 lbs. of essence of widget available per day and the per widget profits are $3, $2, and $4 for types 1, 2, and 3 widgets, respectively, then what is the daily production schedule that maximizes profit? The plant manager has formulated this problem as an LP with initial tableau X3 X4 X5 16 | 1 (essence of widget) (enhancement time) .02 (production time) 10 10 20 0 | 4000 0.03 1 .02 .01 .03 1 | 7 3 4 0. The associated optimal tableau is x3 X4 X5 X6 | (essence of widget) (enhancement time) (production time) 1 .5 .1 -50 150 1 1.5 250 0 -.005 -.001 -.5 1 .5 -1.5 -2 -50 -1050 (a) (15 points) What is the range of the widget enhancement time resource that preserves the currently optimal basis as optimal? (b) (10 points) By how much does this production process increase the value of each hour of widget enhancement time? (c) (10 points) If you could purchase more widget enhancement time, how much more would you be willing to pay for it than you are currently paying, and how many hours should you purchase? (d) (15 points) Do not consider questions (a)-(c) above in answering this question. Due to illness, we expect to loose one hour each of widget enhancement time and widget production time for the next few days. Use the techniques of sensitivity analysis to determine the new production schedule during this time. Hint: The perturbed right-hand side takes the form b+ Ab where Ab = -[0, 1, 1]".
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A 6 Hee Ab B12 R 01 50 0 150 50 R 250 5 150 500 o 2505e 2o 5520 enboe time B9 Keng t wi ... View the full answer
Related Book For
Finite Mathematics and Its Applications
ISBN: 978-0134768632
12th edition
Authors: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
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