Questions from General Calculus

Q: Consider the following problem: A farmer with 750 ft of fencing

Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the la...

Q: Consider the following problem: A box with an open top is

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides....

Q: A farmer wants to fence in an area of 1.5

A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to...

Q: A box with a square base and open top must have a

A box with a square base and open top must have a volume of 32,000 cm3. Find the dimensions of the box that minimize the amount of material used.

Q: If 1200 cm2 of material is available to make a box with

If 1200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Q: A rectangular storage container with an open top is to have a

A rectangular storage container with an open top is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs...

Q: Do Exercise 16 assuming the container has a lid that is made

Do Exercise 16 assuming the container has a lid that is made from the same material as the sides. Exercise 16: A rectangular storage container with an open top is to have a volume of 10 m3. The lengt...

Q: A farmer wants to fence in a rectangular plot of land adjacent

A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neig...

Q: If the farmer in Exercise 18 wants to enclose 8000 square feet

If the farmer in Exercise 18 wants to enclose 8000 square feet of land, what dimensions will minimize the cost of the fence? Exercise 18: A farmer wants to fence in a rectangular plot of land adjacen...

Q: (a) Show that of all the rectangles with a given

(a) Show that of all the rectangles with a given area, the one with smallest perimeter is a square. (b) Show that of all the rectangles with a given perimeter, the one with greatest area is a square....