Question

I'm trying to graph four constraints to get a feasible region for a linear optimization model. I've determined that my constraints are: x + y = 1,000
x >= 250
y >= 250
x >= 2y
I think the values of the constraints in my problem are:
1000 = 1000
667 >= 250
333 >= 250
667 >= 666
Using those, how do I graph those values in my scatterplot to get the feasible region?!?!

Here's the question I'm working with: The Sea Wharf Restaurant would like to determine the best way to allocate a monthly advertising budget of $1,000 between newspaper advertising and radio advertising. Management decided that at least 25% of the budget must be spent on each type of media and that the amount of money spent on local newspaper advertising must be at least twice the amount spent on radio advertising. A marketing consultant developed and index that measures audience exposure per dollar of advertising on a scale from 0 to 100, with higher values implying greater audience exposure. If the value of the index for local newspaper advertising is 50 and the value of the index for spot radio advertising is 80 , how should the restaurant allocate its advertising budget to maximize the value of total audience exposure?

Answer 1

x >= 250 ,

y>= 250

x+y<= 1000

x>= 2y

plot all the lines
x = 250 ,

y = 250 and x = 2y

Minimize Z = 50x + 80y

'

1. To draw constraint x1?250?(1)

Treat it as x1=250

Here line is parallel to Y-axis

x1	250	250
x2	0	1

2. To draw constraint x2?250?(2)

Treat it as x2=250

Here line is parallel to X-axis

x1	0	1
x2	250	250

3. To draw constraint x1-2x2?0?(3)

Treat it as x1-2x2=0

When x1=0 then x2=?

?(0)-2x2=0

?-2x2=0

?x2=0-2=0

When x2=0 then x1=?

?x1-2(0)=0

?x1=0

x1	0	0
x2	0	0

4. To draw constraint x1+x2?1000?(4)

Treat it as x1+x2=1000

When x1=0 then x2=?

?(0)+x2=1000

?x2=1000

When x2=0 then x1=?

?x1+(0)=1000

?x1=1000

x1	0	1000
x2	1000	0