Question

The common region represented by the inequalities x+y≤ 400, 4x≤y x  ≥40 is​

Answer 1

Answer:

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Answer 2

Concept-

For both the given equations, substitute the values of x and y and plot those values in the graph to get the common region.

Given-

Equations are given as x+ y ≤ 400 ; 4x≤y ; x≥40

Find-

Common region to the inequalities by the intersection of given linear equations.

Solution-

Converting the inequalities to equation , we obtain:

x+ y= 400, 4x =y , x=400

x+ y= 400: This line meets x- axis at (0,400) and y- axis at (400,0). Draw a thick line through these points. We see that the origin (0,0) satisfies the inequality x+ y≤ 400. Therefore, the region containing the origin is the solution of the inequality x +y ≤400.

4x=y: This line passes through the origin (0,0). We see that the region above the line satisfies the inequality 4x≤y. Therefore, the region above the origin is the solution of the inequality 4x≤y.

x≥40: This line is parallel to the y- axis. We see that the region to the right of this line satisfies the inequality x≥40. Therefore, the region to the right is the solution of the inequality x≥40.

Hence, the solution to the inequalities is the intersection of the above three solutions.

Thus, the shaded region represents the solution set of the inequalities which lies in first quadrant.

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