# Need Help pronto

##### New member
This is the problem:
A company distributes its product by train and by truck. The cost of distributing by train can be modeled as -0.09x2 + 34x - 100, and the cost of distributing by trucks can be modeled as -0.04x2 + 22x -175, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by trucks.

#### tkhunny

##### Moderator
Staff member
Note: This may be intended as a simple exercise of polynomial subtraction. Just combine like terms and see what you get. We can save the important technical considerations for later, but in the grand scheme of things, there is a whole lot more going on here than a subtraction problem. If it were my assignment, I'd be a whole lot more careful about the problem design.

This is a very tricky problem. You MUST decide what things mean. You may not just assume that these formulae are valid everywhere.

1) We probably should start with x >= 0, since you cannot ship fewer than zero (0) tons.

2) By similar considerations, we cannot ship more than 374 tons by train or 541 tons by truck. If we can, then someone will have to start paying us to use them. This is not reasonable.

3) Noting that trains quit at 374, but trucks continue to 541, there is NOT ANY solution to the problem, as stated, for 374 < x < 542. Don't even try to write one. It doesn't exist.

Having said that, simply subtract. $$\displaystyle (-0.09x^{2} + 34x - 100) - (-0.04x^{2} + 22x - 175) = ??$$. Be very careful with the order of operations and the distributive property and combine like terms. Make sure you agree that this is applicable for only 0 <= x <= 374. It doesn't mean anything for any other value of x.

#### Subhotosh Khan

##### Super Moderator
Staff member
Actually, the lower limit of the domain is not 0.

Staff member
Recievables?

#### tkhunny

##### Moderator
Staff member
tkhunny said:
$$\displaystyle (-0.09x^{2} + 34x - 100) - (-0.04x^{2} + 22x - 175)$$

It dawns on me that the 'x' mightn not be the same for trucks and trains. If you have 100 tons, what's to stop you from shipping 20 by truck and 80 by train?

$$\displaystyle (-0.09Train^{2} + 34Train - 100) - (-0.04Truck^{2} + 22Truck - 175)$$

And we have very little possible simplification.

I just really do not like this problem as it is presented. Can you tell?