A scholarship amount is given by z = 550x + 3 | vedclass

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(A) The feasible region is bounded by the vertices $A, B, C$. From the graph,the lines are $x = 5$,$y = 4$,$x + y = 15$,and $x - y = 10$. $1$. Vertex

Vedclass · Accepted Answer

$7250$

Vedclass · Answer

(A) The feasible region is bounded by the vertices $A, B, C$. From the graph,the lines are $x = 5$,$y = 4$,$x + y = 15$,and $x - y = 10$. $1$. Vertex $A$ is the intersection of $x = 5$ and $x - y = 10$. Substituting $x = 5$,we get $5 - y = 10$,so $y = -5$. However,the region is in the first quadrant,so we look at the intersection of $x = 5$ and $x + y = 15$,which is $(5, 10)$. $2$. Vertex $B$ is the intersection of $x = 5$ and $x + y = 15$,which is $(5, 10)$. $3$. Vertex $C$ is the intersection of $y = 4$ and $x + y = 15$,which is $(11, 4)$. $4$. Vertex $D$ is the intersection of $y = 4$ and $x - y = 10$,which is $(14, 4)$. Wait,looking at the shaded region,the vertices are $A(5, 5)$,$B(5, 10)$,and $C(11, 4)$. - At $A(5, 5)$: $z = 550(5) + 300(5) = 2750 + 1500 = 4250$. - At $B(5, 10)$: $z = 550(5) + 300(10) = 2750 + 3000 = 5750$. - At $C(11, 4)$: $z = 550(11) + 300(4) = 6050 + 1200 = 7250$. The maximum value is $7250$.

$A$ scholarship amount is given by $z = 550x + 300y$ and is to be distributed among $x$ boys and $y$ girls. From the graph given below,the maximum amount of scholarship is . . . . . . .

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