Is my LP model correct?

Question

A Digital Image Printing (DIP) company makes two types of printers: industrial and home printers. The company makes P400 profit from each industrial and a P200 profit from each piece of home printer. The company has a contract to provide a store with exactly 30 printers per month. A separate industrial company supply DIP with at least 80 printer heads per month. DIP must purchase at least this amount but can order more. Each industrial printer requires 2 printer heads; each piece of home printer requires 8 printer heads. From past performance, the shop owners know they cannot make more than 20 industrial printers per month. They want to know the number of printers of each type to produce in order to maximize profit.

Answer 1

I have almost the same constraints except the following

A separate industrial company supply DIP with at least 80 printer heads per month. DIP must purchase at least this amount but can order more. Each industrial printer requires 2 printer heads; each piece of home printer requires 8 printer heads

Since it is "at least" the constraint is $2x+8y\geq 80$.

There are several methods to solve such problems.

$1)$ You are lucky. This problem has only 2 variables. Thus it can be solved graphically. See here how it works. In this case the optimal solution is on the line $y=30-x$

$2)$ You can use a computer program. I have used the web page here. The formulation is

Maximize p = 400x+200y subject to 
x+y=30 
2x + 8y >= 80
x<= 20

Just mark, copy and paste it.

$3)$ It can be solved with the simplex method by yourself. If you want to apply this method and you have questions about it, feel free to ask.