Answer in Operations Research for gunna24 #249769
2.3 Solve the following linear programming graphically [5]
Minimize = 3 + 9
Subject to the constraints: + 3 ≥ 6
+ ≤ 10
≤
≥ 0; ≥ 0
Minimize “ud835udc67 = 3ud835udc65 + 9ud835udc66”
subject to the constraints
“begin{matrix}n x+3ygeq6 \nx+y leq 10 \nx leq y \nxgeq0, ygeq0nend{matrix}”
Find the point(s) of intersection
“y=-dfrac{1}{3}x+2”
“y=-x+10”
“x=0:”
“y=-dfrac{1}{3}(0)+2, Point A(0,2)”
“y=-0+10, Point B(0,10)”
“-dfrac{1}{3}x+2=x”
“dfrac{4}{3}x=2”
“x=1.5, y=1.5,Point D(1.5,1.5)”
“-x+10=x”
“2x=10”
“x=5, y=5,Point C(5,5)”
Point “A(0,2):ud835udc67(0,2) =3(0) + 9(2)=18”
Point “B(0,10):ud835udc67(0,10) = 3(0) +9(10)=90”
Point “C(5,5):ud835udc67(5,5) = 3(5) +9(5)=60”
Point “D(1.5,1.5):ud835udc67(1.5,1.5) = 3(1.5) +9(1.5)=18”
The function “z” has a minimum with value of “18” at “(0,2)” and at “1.5,1.5).”
