# Rei origami swans and giraffes, Linear Programming

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.

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

## 1 Answer

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.