I'm trying to learn how to solve this kind of questions...

First I would like to know the difference between the general and standard LP model. What does it means general and standard?

Second I would like to know if the first part I built is correct.

Follow the question:

A timber mill receives at most 200 metres per day of raw logs to cut up into 'dressed' wood of 3 different sizes. The sizes are in terms of cross-sectional dimensions, namely 4x4, 2x4 and 2x2. Each log can be cut into a single 4x4 or two 2x4s or four 2x2s. A 4x4 piece requires 4 cuts (to trim the round edges of the log). A 2x4 requires 5 cuts and a 2x2 requires 6 cuts. Each cut costs 50 cents and produces 0.25kgs per metre of sawdust. A 4x4 piece can be sold for $30 per metre, a 2x4 for $12 per metre and a 2x2 for 5$ per metre. The 2x2 size is in highest demand. However, although they sell 5 times more 2x4 than 4x4, they never sell more than 100 metres of 2x4 per day. Fortunately, they can also sell all the sawdust to a cat shelter for $5 per 10 kg bag. I need a LP model in both general and standard (or equation) form to maximise profit.

The way that I'm trying to solve the first part.

A timber mill receives at most 200 metres per day of raw logs to cut up into 'dressed' wood of 3 different sizes. The sizes are in terms of cross-sectional dimensions, namely x1, x2 and x3. Each log can be cut into a single x1 or two x2 or four x3.

A x1 piece requires 4 cuts (to trim the round edges of the log).

A x2 requires 5 cuts

A x3 requires 6 cuts.

Each cut costs 50 cents and produces 0.25kgs per metre of sawdust.

A X1 piece can be sold for $30 per metre,

A X2 for $12 per metre

A x3 for 5$ per metre.

The x3 size is in highest demand.

Although they sell 5 times more x2 than x1,

they never sell more than 100 metres of x2 per day.

Fortunately, they can also sell all the sawdust to a cat shelter for $5 per 10 kg bag. Write an LP model in both general and standard (or equation) form to maximise profit.

Maximise: Z = 30X1 + 12X2 + 5X3

Constraints:

X1 + 2X2 + 4X3 <= 200

X2 <=100

X1 <= -X1 + 5X2

X>= 0

X2 >= 0

From the above we know that each log have aprox 4x4. Should I use this info here?