7. A linear programming problem is given as below. What is the optimal solution (X1, X2)? Maximize: Z = 5X1 + 3X2subject to:X1+ X2≤ 12X1+2X2 ≤ 20X2 ≥ 3X1, X2 ≥ 0 Select one:a.(9, 3)b.(20, 0) c.(0, 12) d.(0, 10) e.(4, 8) f.(2, 10)7.

Answered: A linear programming problem is given…

Practical Management Science

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ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

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7. A linear programming problem is given as below. What is the optimal solution (X₁, X₂)?

Maximize: Z = 5X₁ + 3X₂

subject to:

X₁+ X₂≤ 12
X₁+2X₂ ≤ 20
X₂ ≥ 3
X₁, X₂ ≥ 0

Select one:

(9, 3)

(20, 0)

(0, 12)

(0, 10)

(4, 8)

(2, 10)

Expert Solution

WORKING NOTES

NOTE : As no particular method is specified I did in Graphical Method.

MAX zx

subject to

X1	+		X2	≤	12
X1	+	2	X2	≤	20
			X2	≥	3

and X1,X2≥0;

Hint to draw constraints

1. To draw constraint X1+X2≤12→(1)

Treat it as X1+X2=12

When X1=0 then X2=?

⇒(0)+X2=12

⇒X2=12

When X2=0 then X1=?

⇒X1+(0)=12

⇒X1=12

X1	0	12
X2	12	0

2. To draw constraint X1+2X2≤20→(2)

Treat it as X1+2X2=20

When X1=0 then X2=?

⇒(0)+2X2=20

⇒2X2=20

⇒X2=202=10

When X2=0 then X1=?

⇒X1+2(0)=20

⇒X1=20

X1	0	20
X2	10	0

3. To draw constraint X2≥3→(3)

Treat it as X2=3

Here line is parallel to X-axis

X1	0	1
X2	3	3

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