Mr. McGregor design outdoor living spaces intended to attract rabbits. He know t

Question

Mr. McGregor design outdoor living spaces intended to attract rabbits. He know that rabbit weigh lettuce at 5 units of happiness, French bean plants at 3 units of happiness, an radishes at 2 units of happiness. He is subject to the following issues. He only has 37 dollars in his budget, and only has 200 pots to plant in. Lettuce seed packets costs $1.13, and have eight seeds. French bean seed packets cost $2.16 have twelve seeds. Radish seed packets cost $5.19, and have fourteen seeds. Assume each pot gets one seed, and each will germinate. His wife forbids him from planting more than 50 pots of lettuce.
Build a LP that tells how many of each type of seed packet he should buy.

Explanation / Answer

maximize = 5X+3Y+2Z

HERE X=lettuce SEED PACKET

Y=French bean plants SEED PACKET

Z=radishes SEED PACKET

SUBJECTED TO,

8X+12Y+14Z=200

1.13X+2.16Y+5.19Z<=37

X<=50

X,Y,Z >0

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