CODEWITHSUNDEEP
linear-programminglpsolveinteger-programming
Joe Austin
Joe Austin

Reputation: 557

Maximising the benefit of a given scenario

I'm having trouble with a question given to us by my professor:

A husband and wife are going on a trip and wish to maximise the benefit of bringing certain items with them. The husband can bring 20kgs and the wife can bring 17kgs. What should they bring?

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This is what I have written and run using the 'lp_solve' linux command: 

max 10 hs + 9 hl + 6 ha + 3 hb + 14 hr + 10 ws + 9 wl + 6 wa + 3 wb + 14 wr;

7 hs + 6 hl + 13 ha + 4 hb + 9 hr <= 20;
7 ws + 6 wl+ 13 wa + 4 wb + 9 wr <=17;

hs + ws <= 1;
hl + wl <= 1;
ha + wa <= 1;
hb + wb <= 1;
hr + wr <= 1;

bin hs,hl,ha,hb,hr,ws,wl,wa,wb,wr;

And this is my result: Output

My result show that the husband should take the stove and the axe while the wife should take the lamp and the binoculars. This is a valid result but it isn't the most beneficial... Can someone explain to me what I'm doing wrong?

Much appreciated.

Upvotes: 2

Views: 108

Answers (1)

Ram Narasimhan
Ram Narasimhan

Reputation: 22506

Something very subtle is going on. You are missing a colon : after the max. So the lp_solver thinks that max is an unbounded variable. Your objective function value is what tipped me off.

Once you modify your Objective Function to:

max: 10 hs + 9 hl + 6 ha + 3 hb + 14 hr + 10 ws + 9 wl + 6 wa + 3 wb + 14 wr;

You will get the correct solution:

hs, ha, wl and wr will be 1.

Upvotes: 3

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