For the inequalities x+y leq 3,2x+5y geq 10,x | vedclass

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Question

(C) To find the point in the feasible region,we must check which point satisfies all the given inequalities:$1$) $x+y \leq 3$$2$) $2x+5y \geq 10$$3$)

Vedclass · Accepted Answer

$(1,2)$

Vedclass · Answer

(C) To find the point in the feasible region,we must check which point satisfies all the given inequalities:$1$) $x+y \leq 3$$2$) $2x+5y \geq 10$$3$) $x \geq 0, y \geq 0$Let us test the given options:For option $(A)$ $(2,2)$: $2+2 = 4 
ot\leq 3$. (False)For option $(B)$ $(4,2)$: $4+2 = 6 
ot\leq 3$. (False)For option $(C)$ $(1,2)$: $1+2 = 3 \leq 3$ (True),$2(1)+5(2) = 2+10 = 12 \geq 10$ (True),and $1 \geq 0, 2 \geq 0$ (True). (True)For option $(D)$ $(2,1)$: $2(2)+5(1) = 4+5 = 9 
ot\geq 10$. (False)Thus,the point $(1,2)$ satisfies all the inequalities and lies in the feasible region.

For the inequalities $x+y \leq 3$,$2x+5y \geq 10$,$x \geq 0$,$y \geq 0$,which of the following points lies in the feasible region?

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