- #1
Erenjaeger
- 141
- 6
I was given the problem attached in the photo below and the first question is to define the decision variables and formulate the problem as a linear program. There are no solutions online, so it would be helpful if someone on the mighty PF could check them to see if they are correct, thanks.
https://scontent.fhlz2-1.fna.fbcdn.net/v/t34.0-12/23113532_1505762442836859_1149946816_n.png?oh=f7a855d08561239a24b48af9741cbfbf&oe=59FAF30B
decision variables are..
let xig be the amount of time the investor spends gardening
let xwg be the amount of time the worker spends gardening
let xir be the amount of time the investor spends rewiring the house
let xii be the amount of time the investor spends insulating the house
let xcv be the amount of time the contractor spends checking ventilation
Max: 400xig + 400xwg +350xir +200xii + 300xcv - 100xig - 100xir - 60xwg - 150xcv
subject to:
xig + xir + xii ≤ 50
xig ≤ 10
xir ≥ 6
xii / (xig + xwg ) ≥ 2
Note: I'm not that sure about the last constraint, It is meant to be the one that says for 1 hour gardening there has to be at least 30 minutes insulating.
https://scontent.fhlz2-1.fna.fbcdn.net/v/t34.0-12/23113532_1505762442836859_1149946816_n.png?oh=f7a855d08561239a24b48af9741cbfbf&oe=59FAF30B
decision variables are..
let xig be the amount of time the investor spends gardening
let xwg be the amount of time the worker spends gardening
let xir be the amount of time the investor spends rewiring the house
let xii be the amount of time the investor spends insulating the house
let xcv be the amount of time the contractor spends checking ventilation
Max: 400xig + 400xwg +350xir +200xii + 300xcv - 100xig - 100xir - 60xwg - 150xcv
subject to:
xig + xir + xii ≤ 50
xig ≤ 10
xir ≥ 6
xii / (xig + xwg ) ≥ 2
Note: I'm not that sure about the last constraint, It is meant to be the one that says for 1 hour gardening there has to be at least 30 minutes insulating.