Optimization Help

[v1ru5]

I was having some problems with this question wondering if anyone could help me.

A truck delivers cargos at a constant speed of 110km/h gets gas mileage of 10 km/L. Gas costs $1.20/L. THe truck loses 0.10 km/L in fuel efficiency for each km/h increase in speed. The driver is paid $32/h in wages. Fixed costs for running the truck are $16/h. If a trip of 400 km is planned, what speed will minimize the operation expenses? Hint: Total cost = Labour cost + fixed cost + gas cost.

So here is what I was able to do:

Let t represent the amount of time travelled in hours
Let s represent the speed increase of 1km/h

Gas cost = (110 + s)(10-0.10s) I am confused here I am not really sure what I am supposed to do to find the gas cost

TotalCost = 32t + 16t + gas cost

Any help would be greatly appreciated.

Thanks

 

[tkhunny]

This is a very oddly-stated problem. Neither 32t nor 16t represents a FIXED cost. The taxes to own the truck for a year would be a FIXED cost. The space to park the truck would be a FIXED cost.

In any case: Distance = Rate * Time is the only piece you are missing. This will help you express s in terms of t, or vice versa.

 

[v1ru5]

This is a very oddly-stated problem. Neither 32t nor 16t represents a FIXED cost. The taxes to own the truck for a year would be a FIXED cost. The space to park the truck would be a FIXED cost.

In any case: Distance = Rate * Time is the only piece you are missing. This will help you express s in terms of t, or vice versa.

okay i was able to get the gas cost by doing this: 400km*(1/10-0.1s)*1.20 which is basically 480/10-0.1x

All units cancel out except for cost so I am left with $

So my equation i have was Total cost = 16t + 32t + gas cost

then t = 400/(110+ x)

replace t with that in the total cost equation find the derivative set it to zero and solve. But for some reason i am getting a negative square root when i set the derivative = 0 so I probably did something wrong but im not sure.

 

[tkhunny]

Let's think about this:

(110 + s)(10-0.10s)

Units will save you.

110 is km/h

s is km/h

10 is km/L

0.10 is km/L, so 0.10s is (km/L)*(km/h) = (km^2)/(L*h) -- ???? What is that?

Let's redefine 's' to be just a number, not carrying the units along with it.

-------------------------------------------------------------------------------------------

Distance = Rate * Time

Distance = 400 km

Rate = (110 + s) km/h

------------------------------------------------------------------------------------------
Now what?