Consider the following linear programming problem Min A+ 2B s.t. A + 4B< or equa

Question

Consider the following linear programming problem

Min A+ 2B
s.t.
A + 4B< or equal to 21
2A + B > or equal to 7
3A + 1.5B < or equal to 21
-2A + 6B > or equal to 0
A, B > or equal to 0

a. Find the optimal soulution using the graphical soulution procedure and the value of the objective function


b.determine the amount of slack or surplus for each constraint
(dont worry about this problem it has been emitted from the homework but if you can help me to understand this I would greatly apprecaite it)

c. suppose the objective function is changed to max 5A+2B. Find the optimal solution and the value of the objective function.

.

Explanation / Answer

this is quite a simple question. Now on plotting the graph for the inequalities we ll get the graph in 1st quadrant since A,B > 0 and if you plot all the above inequlities the minimum y-intercept is 7. so the min of A+2B = 7

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