Question

Sprout problem: California farmer of sprouts deals mainly with alfalfa sprouts and brussels sprouts. He has hired you to optimize his profits and offers you 40% as your salary. Let X= Number of pounds of alfalfa sprouts and y= Number of pounds of brussels sprouts the parameters are as follows

x+y<=30
x<=30, x>=3
y<=20
5x+12y<=300
5x-6y<=60
plot these inequalities and shade the feasible region

Answer 1

see attached

Explanation:

In the attached, the feasible region is white, and all excluded regions are shaded. When there are so many inequalities, it is easier to see the solution (feasible region) this way. The boundary lines are dashed because they are not excluded. That is, each boundary line is part of the feasible region.

The vertices of the feasible region are shown to aid in any optimization you might want to do. We have shown the values that would apply if there were a constraint y ≥ 0, which is not on your list. (We assume pounds of Brussels sprouts will not be negative.)

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If you actually do the shading required by the problem statement, you will be shading on the opposite side of each of the lines shown, and you would draw the lines as solid.