A rectangular box with no top is to have a square base and a volume of 10 ft. The material for the base costs 29 cents/ft and the material for the sides costs 18 cents/ft. If denotes the length of one side of the base (in feet), find a function in the variable giving the total cost of materials used in constructing the box in cents.

The weekly supply function for high definition televisions is given by where is the number of thousands of televisions and is in dollars. Find the average rate of change of the unit price as the quantity supplied goes from 5000 televisions to 5500 televisions.

The weekly supply function for radial tires is given by where is the number of thousands of tires and is in dollars. Find the average rate of change of the unit price as the quantity supplied goes from 2000 tires to 2500 tires.  

A rectangular box is to have a square base and a volume of 30 ft. The material for the base costs 17 cents/ft, the material for the top costs 11 cents/ft, and the material for the sides costs 12 cents/ft. If denotes the length of one side of the base (in feet), find a function in the variable giving the total cost of materials used in constructing the box in cents.

A billboard designer has decided that a sign should have 4-ft margins at the top and bottom and 5-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 550 ft (including the margins). If denotes the width (in feet) of the billboard, find a function in the variable giving the area of the printed region of the billboard.

A rectangular box is to have a square base and a volume of 20 ft. The material for the base costs 25 cents/ft, the material for the top costs 15 cents/ft, and the material for the sides costs 16 cents/ft. If denotes the length of one side of the base (in feet), find a function in the variable giving the total cost of materials used in constructing the box in cents.

A billboard designer has decided that a sign should have 3-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 700 ft (including the margins). If denotes the width (in feet) of the billboard, find a function in the variable giving the area of the printed region of the billboard.

A rectangular box with no top is to have a square base and a volume of 10 ft. The material for the base costs 19 cents/ft and the material for the sides costs 12 cents/ft. If denotes the length of one side of the base (in feet), find a function in the variable giving the total cost of materials used in constructing the box in cents.

The weekly supply function for radial tires is given by where is the number of hundreds of tires and is in dollars. Find the average rate of change of the unit price as the quantity supplied goes from 200 tires to 250 tires.

The weekly supply function for video game consoles is given by where is the number of hundreds of consoles and is in dollars. Find the average rate of change of the unit price as the quantity supplied goes from 300 consoles to 350 consoles.