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.

By cutting away an -by- square from each corner of a rectangular piece of cardboard and folding up the resulting flaps, a box with no top can be constructed. If the piece of cardboard is 32 inches long by 26 inches wide, find a function in the variable giving the volume of the resulting box.

A billboard designer has decided that a sign should have 2-ft margins at the top and bottom and 4-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 800 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 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 650 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 30 ft. The material for the base costs 24 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 rectangular box is to have a square base and a volume of 20 ft. The material for the base costs 20 cents/ft, the material for the top costs 13 cents/ft, and the material for the sides costs 10 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 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.

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

A rectangular box with no top is to have a square base and a volume of 50 ft. The material for the base costs 16 cents/ft and the material for the sides costs 10 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 term for the total heat production by the body is: