Answered: MIn 150x+210y s.t. 3.8x+ 1.2y>=22.9…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

MIn 150x+210y

s.t.

3.8x+ 1.2y>=22.9

y>=5

y<=13

45X-30Y=255

X,Y>=0

Solve the linear problem graphically

(X,Y)=( )

How many extreme points exist for this problem

Expert Solution

WORKING NOTES

MIN Zx

150

210

subject to

3.8	x	+	1.2	y	≥	22.9
				y	≥	5
				y	≤	13
45	x	-	30	y	=	255

and x,y≥0;

Hint to draw constraints

1. To draw constraint 3.8x+1.2y≥22.9→(1)

Treat it as 3.8x+1.2y=22.9

When x=0 then y=?

⇒3.8(0)+1.2y=22.9

⇒1.2y=22.9

⇒y=22.91.2=19.08

When y=0 then x=?

⇒3.8x+1.2(0)=22.9

⇒3.8x=22.9

⇒x=22.93.8=6.03

x	0	6.03
y	19.08	0

2. To draw constraint y≥5→(2)

Treat it as y=5

Here line is parallel to X-axis

x	0	1
y	5	5

3. To draw constraint y≤13→(3)

Treat it as y=13

Here line is parallel to X-axis

x	0	1
y	13	13

4. To draw constraint 45x-30y=255→(4)

Treat it as 45x-30y=255

When x=0 then y=?

⇒45(0)-30y=255

⇒-30y=255

⇒y=255-30=-8.5

When y=0 then x=?

⇒45x-30(0)=255

⇒45x=255

⇒x=25545=5.67