A farmer has to transport 20 people and 32 sheep to a market. He can use either Fiats (x) which take 2 people and 1 sheep, or Rolls Royce (y) which take 2 people and 4 sheeps. He must not use more than 15 cars altogether.
a) What is the lowest total numbers of cars he could use?
b) If it costs $10 to hire each Fiat and $30 for each Rolls Royce, what is the cheapest solution?

Question

A farmer has to transport 20 people and 32 sheep to a market. He can use either Fiats (x) which take 2 people and 1 sheep, or Rolls Royce (y) which take 2 people and 4 sheeps. He must not use more than 15 cars altogether.
a) What is the lowest total numbers of cars he could use?
b) If it costs $10 to hire each Fiat and $30 for each Rolls Royce, what is the cheapest solution?

anonymous · Answer

Please help if possible, this is really urgent! Thanks

anonymous · Answer

It relates to linear programming.

tylerd · Answer

ok well
X = 2p+s
Y= 2p+4s

aX+bY= 20p+32s

a+b=15

tylerd · Answer

maybe that could get us started

tylerd · Answer

i guess we should say $$a+b \le 15$$

tylerd · Answer

@aum

anonymous · Answer

Oh forgive me but I forgot to add that the answer for a) is 10. I need to know how to get there.

anonymous · Answer

I should have said that earlier and b) is 250, (4,7).

tylerd · Answer

so you already solved it?

anonymous · Answer

no, it is at the back of the textbook

anonymous · Answer

i have access to answers but not how to solve them.

tylerd · Answer

ive got no clue about linear programming but for some reason i feel like this involves graphing.

anonymous · Answer

I believe it does too, that is what linear programming has to do with in my curriculum.

anonymous · Answer

I guess i just need to know sufficient inequalities to graph them.

aum · Answer

Assume 'F' Fiats and 'R' Rolls Royces.
Each Fiat can transport 2 people and each Rolls can transport 2 people.
2F + 2R >= 20 people
F + R >= 10   ---- (1)

Each Fiat can transport 1 sheep and each Rolls can transport 4 sheeps.
F + 4R >= 32 ---- (2)

Minimize F+R.   From (1) it looks like the minimum is 10.

anonymous · Answer

Oh wow, that helps a lot, thank you, now if you can just help with b)

tylerd · Answer

+fan dude, now im gonna pass out

anonymous · Answer

hahaha

aum · Answer

For b) minimize 10F + 30R

anonymous · Answer

F+3R

anonymous · Answer

then what do i do?

aum · Answer

They ask for the cheapest solution so you have to find the minimum value of 10F+30R.

anonymous · Answer

and for that, i guess i must draw a graph

aum · Answer

yes.  Treat F as y and R as x.

anonymous · Answer

oh thanks so much, you guys have been a great help

aum · Answer

You are welcome.  What is the book answer for b)?

anonymous · Answer

I shall take it from here thanks.

anonymous · Answer

240, (4,7)

anonymous · Answer

this has proves to be a great website so far, i just started today.

anonymous · Answer

Thanks once again, I am a fan...literally!

aum · Answer

You are very welcome.  Glad to be able to assist.

anonymous · Answer

Bye! I am closing now