PCB Chemicals

PCB chemicals of Florida makes various chemical compounds. One compound is Bug Stomper

insecticide. Bug stomper is used to ward off the dreaded Florida Palmetto Bugs. A palmetto bug is like a

$3$ inch long cock roach on steroids, that smells bad, can fly, and is extremely aggressive. They typically

come out at night from behind the frig and like to fly into people$$s faces. PCB also makes the plastic jugs

bug stomper is sold in$.$ Plastics jugs are made in one location, filled in another and then sent to a

distribution center for sale to local exterminators.

Plastic jugs are made in Tampa and Jacksonville. The process takes poly resin pellets from a train car

melts them and injection molds a jug. The gallon jug is then tested for quality by measuring the

thickness of the plastic at bend points and pressurizing the jug with air to see if it leaks. Jugs are then

put in a chamber and reheated and flooded with fluorine gas to seal the plastic $($else the bug stomper

juice would eat through the jug$).$ It costs $$\mathrm{.}35$ to mold a jug in Tampa and $$\mathrm{.}25$ to mold a jug in

Jacksonville. Each plant can mold $150,000$ jugs a month. The molded jugs are placed in train cars and

sent to filling plants in Plant City, Tallahassee and Yehaw Junction.

At the filling plants the jugs are filled with bug stomper and labeled. It costs $$\mathrm{.}9$ to fill a jug in Plant City,

$$1\mathrm{.}25$ to fill one in Tallahassee, and $$1\mathrm{.}00$ to fill one in Yehaw Junction. Each filling plant can fill $75,000$

jugs a month. The filled jugs are sent to the distribution centers in Tampa $($separate facility from jug

molding$),$ Orlando, Miami and Panama City. Next month$$s demand is as follows

Gallon Jugs

Tampa $50,000$

Orlando $40,000$

Miami $70,000$

Panama City $30,000$

Shipping costs for empty jugs are as follows

Cost Per jug $

To

From Plant City Tallahassee Yehaw Junction

Tampa $\mathrm{.}05\mathrm{.}2\mathrm{.}15$

Jacksonville $\mathrm{.}2\mathrm{.}06\mathrm{.}22$

Shipping costs for filled jugs are as follows

Cost per Jug $

To

From Tampa Orlando Miami Panama City

Plant City $\mathrm{.}1\mathrm{.}1\mathrm{.}3$ CGTFH

Tallahassee $\mathrm{.}2\mathrm{.}15\mathrm{.}4\mathrm{.}1$

YehawJunction CGTFH $\mathrm{.}1\mathrm{.}2\mathrm{.}3$

CGTFH $=$ Can$$t get there from here.

PCB needs to know what the most cost effective plan would be to meet next month$$s demand. How

many jugs should be molded at each molding plant, where should they be sent? How many jugs will

each filling plant fill, where will they be sent. How much will it cost$?$ What will be the overall average

cost per jug when all jugs have arrived at the distribution centers?