Question

Please correct anything inaccurate or missing. Also, if I input it and it's incorrect, it would be nice if you could further help after I let you know in the comments.

Problem 3-01 Consider the following linear program: Max 3A 2B 1A + 1B S 10 3A 1B S 24 1A 2B S 16 A, B 2 O a. Choose the correct graph which represents the optimal solution 26 24 26 20 1S 16 14 12 10 18 16 14 10 Optimal Solution A-7, B 3 3A2B 27 Optimal Solution A 6.4, B 4.8 3A 2B 28.8 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 (ii) 26t (iv) ,43 26 24 20 20 18 16 16 14 12 A 0B 10 10* 3A + 2B 20 Optimal Solution 12 10 Optimal Solution A 10, B 0 3A2B 30 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20

Answer 1

Answer:

a)

Option i.

Explanation:

• All the graphs represent the three constraint lines but if you notice all the constraints have less than equal to sign, which means that the feasible region is from the line towards origin.
• So if you see in the four option only such feasible region (towards origin) for all the lines, is in option 1 and its perfectly the right graph.

b)

• A =7
• B=3
• Optimal solution = 27

Explanation:

• As you can se in graph of option i in question a, Point of intersection are:
  • A=4 and B= 6 (intersection of constraint line 1 and 3 by equating both)
  • A= 7 and B= 3 (intersection of constraint line 1 and 2 by equating both)
• The points of intersection in the feasible region the point giving max value is A=7, B=3. Putting the values in objective function, optimal solution =27.

c)

• A=4
• B=6
• OS =36

Explanation:

• Point of intersection are:
  • A=4 and B= 6 (intersection of constraint line 1 and 3)
  • A= 7 and B= 3 (intersection of constraint line 1 and 2)
• New Objective function = 3A +4B
• So the values with each point of intersection are :
  • 33 with (7,3)
  • 36 with (4,6)
• Hence A= 4 and B=6 and OS = 36

D)

• For A from 2.00 to 6.000
• For B from 1.00 to 3.000

Explanation:

• Range = from (coefficient - allowable decrease) to (coefficient +allowable increase)
• A = from (3-1) to (3+3)= from 2 to 6
• B= from (2-1) to (2+!) = from 1 to 3