Linear Programming

Linear Programming

(Worksheet problems)

#4
Vertices:	(0,0)		(0,6)		(6,0)
Constraints	Objective Function: C= 3x+4y
x ≥ 0 y ≥ 0 x + y ≤ 6	C=3x+4y C=3(0)+4(0) C=0	C=3x+4y C=3(0)+4(6) C=24		C=3x=4y C=3(6)+4(0) C=18

#5
Vertices:	(-5,4)		(5, 4)		(5, 8)
Constraints	Objective Function: C=2x+5y
x ≤ 5 y ≥ 4 -2x +5 y ≤ 30	C=2x+5y C=2(-5)+5(4) C=10	C=2x+5y C=2(5)+5(4) C= 30		C=2x+5y C=2(5)+5(8) C=50

# 6
Vertices:	(1, 2)		(5,2)		(1,8)
Constraints	Objective Function: C= 7x+3y
x ≥ 1 y ≥ 2 6x +4 y ≤ 38	C= 7x+3y C=7(1)+3(2) C= 13	C=7x+3y C=7(5)+3(2) C= 41		C= 7x+3y C=7(1)+3(8) C= 31

#7
Vertices:	(0, 4)		(0, 8)		(6, 8)
Constraints	Objective Function: C= 4x+6y
x ≥ 0 y ≤ 8 -2x + 3y ≥ 12	C= 4x+6y C=4(0)+6(4) C= 24	C=4x+6y C=4(0)+6(8) C= 48		C= 4x+6y C=4(6)+6(8) C= 72

#8
Vertices:	(0,0)		(5,0)		(2,3)		(0,4)
Constraints	Objective Function: C= 8x+7y
x ≥ 0 y ≥ 0 x + y ≤ 5	C= 8x+7y C=8(0)+7(0) C=0	C=8x+7y C=8(5)+7(0) C=40		C= 8x+7y C=8(2)+7(3) C=37		C= 8x+7y C=8(0)+7(4) C=28

#9
Vertices:	(0,2)		(3,0)		(4,3)		(0,4)
Constraints	Objective Function: C= 3x+5y
x ≥ 0 y ≥ 0 x + y ≤ 5	C= 3x+5y C=3(0)+5(2) C=10	C=3x+5y C=3(3)+5(0) C= 9		C= 3x+5y  C=3(4)+5(3) C=27		C=3x+5y C=3(0)+5(4) C=20