A package delivery service has a truck that can hold 4200 pounds of cargo and has a capacity of 480 cubic feet. The service handles two types of packages: small, which weigh up to 25 pounds each and are no more than 3 cubic feet each; and large, which are 25 to 50 pounds each and are 3 to 5 cubic feet each. The delivery service charges $5 for each small package and $8 for each large package. Let x be the number of small packages and y be the number of large packages in the truck.
a. Write an inequality to represent the weight of the packages in pounds the truck can carry.
b. Write an inequality to represent the volume, in cubic feet, of packages the truck can carry.
c. Graph the system of inequalities.
d. Write a function that represents the amount of money the delivery service will make on each truckload.
e. Find the number of each type of package that should be placed on a truck to maximize revenue.
f. What is the maximum revenue per truck?
g. In this situation, is maximizing the revenue necessarily the best thing for the company to do? Explain.