Given the following linear program:
MAX 5x1 + 7x2
s.t.x1 < 6
2x1 + 3x2 < 19
x1 + x2 < 8
x1,x2 > 0
The graphical solution to the problem is shown below.From the graph we see that the optimal solution occurs at x1 = 5,x2 = 3,and z = 46. 
a.Calculate the range of optimality for each objective function coefficient.
b.Calculate the dual price for each resource.
Definitions:
Mouth
The opening in the face of humans and many animals, used for eating, breathing, and speaking, encased by the lips and leading to the throat and digestive tract.
Innate Preference
A natural or instinctual liking or inclination towards something without the need for learning or experience.
Sweet
A taste sensation that is pleasant and often associated with sugary substances.
Salty
A taste sensation primarily produced by the presence of sodium ions in food; colloquially can describe a feeling of bitterness or irritation.
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