Aaargh.. Linear Programming..?

Question

Okay, for anyone that is good at linear programming, I have a question. Well, there's this problem I'm stuck on, and I need help on a few things on it. Here's the problem:
X is the mathematician for Y's Oil Refinery. Y can buy Texas oil, priced at $30 a barrel, and California oil, priced at $15 per barrel. He consults X, the mathematician, to find out what is the most he might have to pay in a month for the oil the refinery uses. Sabrina finds the following restrictions on the amounts of oil that can be purchased in a month. The refinery can handle as much as 40,000 barrels per month.
To stay in business, the refinery must process at least 18,000 barrels a month. California oil has 6 pounds of impurities per barrel, while Texas oil has 2 pounds. The most the refinery can handle is 120,000 pounds of impurities a month. Y spends at least $660,000 per month buying oil.

What would be the constraints for this problem? That's all I need to know. I think I did something wrong.

Thanks

X = "Sabrina", Y = "Pedro". You don't need the names, I just wanted to save space.

Answer 1

let:
Qc be the quantity of California oil to buy (to be determined)
Qt be the quantity of Texas oil to buy (ditto)
Cc and Ct be the costs per barrel of California and Texas oils (known constants)
Ic and It be the pounds of impurities per barrel of the two (known constants)

Then:

total cost = Qc x Cc + Qt x Ct
total impurities = Qc x Ic + Qt x It

The constraints are:

Qc + Qt <= 40,000
Qc + Qt >= 18,000

Qc x Ic + Qt x It <= 120,000

However, the problem is strange as it is not at all clear what function is to be maximized or minimized.

Under most circumstance, you would want to maximize profit, but that depends on the selling price, which we are not given.

Also, the phrase "to stay in business" makes no sense, because surely, since California and Texas crude have different costs, the break-even point must depend on the relative quantities.

Perhaps you know something about the problem that you haven't included?

If not, my guess is that the goal is to minimize cost while maintaining maximum output, but then the quantity constraints become one:

Qc + Qt = 40,000

(If you try to minimize cost without changing the constraint, you end up with Qc + Qt = 18,000 because fewer barrels are cheaper.)