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Rei volunteers to bring origami swans and giraffes to sell at a charity crafts fair. It takes her three minutes to make a swan and six minutes to make a giraffe. She plans to sell the swans for $\$4$ dollars each and the giraffes for $\$6$ each. If she only has $16$ pieces of origami paper and can’t spend more than one hour folding, use a geometric approach to find how many of each animal should Rei make to maximize the charity’s profit?

So far, I have:

s: $\#$ of swans

g: $\#$ of giraffe

p: profit, p= 4s+6g

Constraints:

time it takes to make origami (in minutes): 3s+6g $ \leq$ 60

paper: s+g=16

Number of swans: s $\geq$ 0

Number of giraffes: g $\geq$ 0

After this I am unsure as to where to go. We are instructed that we are to use LINGO, but I am unsure how to use the program nor has the teacher taught us, any help is appreciated and thank you.

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    $\begingroup$ Test for profit at the vertices of this graph. $\endgroup$ Jun 23, 2020 at 23:04
  • $\begingroup$ Why don´t you give any reply (including accepting an answer)? This behaviour doesn´t motivate people to help you. $\endgroup$ Jul 6, 2020 at 5:44

1 Answer 1

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If you are to use a geometric approach, I would make the number of swans the horizontal axis and the number of giraffes the vertical axis. Each constraint is a line that divides the feasible from unfeasible region. The sheets of paper form the line $s+g=16$ and the feasible region is below the line. There is another line for the maximum time folding, plus $s \ge 0, g \ge 0$. That gives you a feasible quadrilateral. Now you know the optimal point is at one of the corners of the region, so compute the profit at each one and you have the best point.

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