Liz Energy drink is to be sold in 472 mL cylindrical cans. Since it is a new product the package designers want the cans to be more visible when displayed with competing products so they want the height of the can to be no less than 12 cm. Determine the dimensions of the can that will minimize the surface area.

Solver Options

Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling

Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name Original Value Final Value

$D$3 area 345.4542674 345.4542674

Variable Cells

Cell Name Original Value Final Value Integer

$D$4 r 3.53838381 3.53838381 Contin

$D$5 h 12 12 Contin

Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling

Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name Original Value Final Value

$D$3 area 345.4542674 345.4542674

Variable Cells

Cell Name Original Value Final Value Integer

$D$4 r 3.53838381 3.53838381 Contin

$D$5 h 12 12 Contin

The answer is Radius of the base = 3.54 cm

Height 12 cm and min surface area = 345.45

Volume 472 cm3

Constraints

Cell Name Cell Value Formula Status Slack

$D$6 volume 472.0000153 $D$6=472 Binding 0

$D$5 h 12 $D$5>=12 Binding 0

## Comments