Sue sells six selections of sea shells on the sea shore. Her selections include large-cone shells, medium-cone shells, small-cone shells, large-flat shells, medium-flat shells, and small-flat shells. Sue hires shell collectors and has 8 labor hours available. The time it takes to collect and inventory each type of shell and the profits for each type are as follows:
Shell-Type Time (minutes) Profit
Large-cone 4 $3.00
Medium-cone 7 $4.50
Small-cone 2 $2.50
Large-flat 3 $4.00
Medium-flat 6 $3.50
Small-flat 2 $1.25
Sue’s sea shells sales slump with a small selection of shells so she must have an equal number of cone shaped shells and flat shaped shells, and each type of shell must number no more than twice the amount of any other shell. Also, broken sea shells don’t get sold, so you cannot sell a fraction of a shell.
(a) Express the objective function and all the constraints.
(b) How many of each type of shell should she keep in inventory to maximize profits? What is her total profit?
(c) Are any of the constraints non-binding? Which ones?
(d) Sue can hire one hour of overtime labor. What is the maximum she should pay for an additional hour of labor?