Question

3. A large box is made from a piece of cardboard that measures 10ft by 10ft . Squares of equal size (side length x) will be cut out of each corner. The sides will then be folded up to form a rectangular box.

a) Write down a formula for V(x), the volume of the cardboard box.

b) What are the critical values for V(x)?

c) What size square should be cut from each corner to obtain maximum volume?

d) What is that maximum volume?

4. Weyland-Yutani has started to get into the smartphone business. Currently there is a uniform annual demand for 9000 W-Y phones. It costs $5 to store a single smartphone for an entire year. And it costs $2500 to set up the assembly line to manufacture a run of phones. Let x = the number of phones made in each run.

a) How many runs are carried out each year (in terms of x)?

b) What is the formula for C(x), the total annual costs associated with storage and setting up the line?

c) Find the value of x which minimizes C(x).

d) Write the minimum value of C(x).

show work please

Answer 1