Mathematics

Problem

A beverage company plans to produce cylindrical cans that must contain exactly

1000\text{ cm}^3

of liquid. The aluminum for the curved side surface costs \

0.02 per square centimeter, while the aluminum for each circular end costs

0.03 per square centimeter. (a) Write an expression for the total manufacturing cost

C

of a single can in terms of the radius

r

(cm) and height

h

(cm). (b) Eliminate one variable using the fixed-volume requirement and rewrite

C

as a function of a single variable. (c) Determine the radius and height that minimize the cost of one can. Clearly indicate the test you use to confirm that your result is a minimum. (d) Using your optimal dimensions, compute the minimum possible cost per can, rounded to the nearest cent, and explain its significance for budgeting. a. Part (a) -- formulate

C(r,h)

b. Part (b) -- express

C

in one variable c. Part (c) -- locate and justify the minimum d. Part (d) -- interpret the minimized cost

Browse the problem library