a)  Profit=1000x+500y

b)  profit > 15000

1000x+500y>15000

divide both sides by 100

10x+5y>150

divide both sides by 5

2x+y>30

I have to draw the line 2x+y=30 first

When x=0 y= 30

When y=0 x=15

plot these points and joint them with a line.

Colour the area to the right of the line.  That is where profit is >30   (as shown in the diagram)

now if you look at parallel lines to this one then you get other lines that represent given profits

Optimal number is 16 large and 14 small  machines

 Profit=1000x+500y

Maximum Profit = 1000*16+500*14

$${\mathtt{1\,000}}{\mathtt{\,\times\,}}{\mathtt{16}}{\mathtt{\,\small\textbf+\,}}{\mathtt{500}}{\mathtt{\,\times\,}}{\mathtt{14}} = {\mathtt{23\,000}}$$  dollars

Very nice, Melody......