Answer: Choice A) max = 56, min = 9
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Explanation:
With linear programming problems like this, the idea is to plot the feasible region, determine the vertices, and use them to figure out which vertex leads to the min and which vertex leads to the max.
Luckily, the first two steps of finding the diagram and vertices have been done for us already. At this point, all you need to do is plug in each vertex one at a time into the objective function z = 3x+5y
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The vertex points, or corner points, are: (0,7),(7,7),(7,3),(3,0), and (0,3)
We'll plug them in one at a time. Then we'll see which z value is the smallest and which is the largest
Plug in (x,y) = (0,7)
z = 3x+5y
z = 3(0)+5(7)
z = 0+35
z = 35
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Plug in (x,y) = (7,7)
z = 3x+5y
z = 3(7)+5(7)
z = 21+35
z = 56
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Plug in (x,y) = (7,3)
z = 3x+5y
z = 3(7)+5(3)
z = 21+15
z = 36
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Plug in (x,y) = (3,0)
z = 3x+5y
z = 3(3)+5(0)
z = 9+0
z = 9
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Plug in (x,y) = (0,3)
z = 3x+5y
z = 3(0)+5(3)
z = 0+15
z = 15
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Summary:
The largest z value we got was z = 56, so this is the max value. It occurs at (x,y) = (7,7)
The smallest z value we got was z = 9, so this is the min value. It occurs at (x,y) = (3,0)
So that's why the final answer is choice A
