Question

A box is constructed out of two different types of metal. The
metal for the top and bottom, which are both square, costs $2 per
square foot and the metal for the sides costs $6 per square foot.
Find the dimensions that minimize cost if the box has a volume of
15 cubic feet. Length of base *x*= ___Height of side
*z*=___

The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 320 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 4 dollar increase in rent. Similarly, one additional unit will be occupied for each 4 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Answer #1

A box is contructed out of two different types of metal. The
metal for the top and bottom, which are both square, costs $2 per
square foot and the metal for the sides costs $2 per square foot.
Find the dimensions that minimize cost if the box has a volume of
25 cubic feet. Length of base x= Height of side z=?

The manager of a large apartment complex knows from experience
that 90 units will be occupied if the rent is 300 dollars per
month. A market survey suggests that, on the average, one
additional unit will remain vacant for each 1 dollar increase in
rent. Similarly, one additional unit will be occupied for each 1
dollar decrease in rent. What rent should the manager charge to
maximize revenue?

The manager of a large apartment complex knows from experience
that 80 units will be occupied if the rent is 368 dollars per
month. A market survey suggests that, on the average, one
additional unit will remain vacant for each 8 dollar increase in
rent. Similarly, one additional unit will be occupied for each 8
dollar decrease in rent. What rent should the manager charge to
maximize revenue?

The manager of a large apartment complex knows from experience
that 100 units will be occupied if the rent is 340 dollars per
month. A market survey suggests that, on the average, one
additional unit will remain vacant for each 10 dollar increase in
rent. Similarly, one additional unit will be occupied for each 10
dollar decrease in rent. What rent should the manager charge to
maximize revenue?

The manager of a large apartment complex knows from experience
that 110 units will be occupied if the rent is 468 dollars per
month. A market survey suggests that, on the average, one
additional unit will remain vacant for each 9 dollar increase in
rent. Similarly, one additional unit will be occupied for each 9
dollar decrease in rent. What rent should the manager charge to
maximize revenue?

A large shipping crate is to be constructed in a form of a
rectangular box with a square base. It is to have a volume of 441
cubic feet. The material for the base of the crate is steel that
costs $6 per square foot, the rest of the crate is constructed out
of wood. The wood for the top of the crate is less expensive at $3
per square foot and the sides will be constructed from the wood...

A box of volume 36 m3 with square bottom and no top
is constructed out of two different materials. The cost of the
bottom is $40/m2 and the cost of the sides is
$30/m2 . Find the dimensions of the box that minimize
total cost. (Let s denote the length of the side of the
square bottom of the box and h denote the height of the
box.)
(s, h) =

Problem: A box with an open top is to be constructed from a
square piece of cardboard, with sides 6 meters in length, by
cutting a square from each of the four corners and bending up the
sides. Find the dimensions that maximize the volume of the box and
the maximum volume.

A closed rectangular box is to contain 12 ft^3 . The top and
bottom cost $3 per square foot while the sides cost $2 per square
foot. Find the dimensions of the box that will minimize the total
cost.

A rectangular box is to have a square base and a volume of 48
ft3. If the material for the base costs 4 cents per square foot,
material for the top costs 20 cents per square foot, and the
material for the sides costs 16 cents per square foot, determine
the dimensions of the square base (in feet) that minimize the total
cost of materials used in constructing the rectangular box.

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