You would like to pour a cement driveway. You want the cement to be 4 inches deep. You measure your driveway and find out it is 30 feet by 40 feet. You call the cement company and find that your cost for cement is $106 per cubic yard with a $25 fee for each truck load for delivery. Each truck can haul a maximum of 12 cubic yards. What is your cost going to be to pour the cement? (You can assume that they can supply any portion of a yard of cement so you don't have to round them.)

Question

You would like to pour a cement driveway. You want the cement to be 4 inches deep. You measure your driveway and find out it is 30 feet by 40 feet. You call the cement company and find that your cost for cement is $106 per cubic yard with a $25 fee for each truck load for delivery. Each truck can haul a maximum of 12 cubic yards. What is your cost going to be to pour the cement?  (You can assume that they can supply any portion of a yard of cement so you don't have to round them.)

anonymous · Answer

Cost = Price/yd^3 * yd^3 purchased + Truck Fee * Truck loads
Let v = volumn of cement required in yd^3
$$v=\frac{(30*40*1/3)}{3^3}=\frac{400}{27} $$
$$\text{Cost}=106*v+25*\text{Ceiling}[v/12]\text{ =}\frac{43750}{27}= 1620.37 \text{ dollars} $$
Where 
$$\text{Ceiling}\left[\frac{\frac{400}{27}}{12}\right]= \text{Ceiling}[1.23]= 2 $$