The Philbrick Company has two plants on opposite sides of

the United States. Each of these plants produces the same two prod$-$

ucts and then sells them to wholesalers within its half of the coun$-$

try. The orders from wholesalers have already been received for the

next $2$ months $($February and March$),$ where the number of units

requested are shown below. $($The company is not obligated to com$-$

pletely fill these orders but will do so if it can without decreasing its

profits.$)$

Plant $1$ Plant $2$

Product February March February March

$13,6006,3004,9004,200$

$24,5005,4005,1006,000$

Each plant has $20$ production days available in February and $23$

production days available in March to produce and ship these prod$-$

ucts. Inventories are depleted at the end of January, but each plant

has enough inventory capacity to hold $1,000$ units total of the two

products if an excess amount is produced in February for sale in

March. In either plant, the cost of holding inventory in this way is

$$3$ per unit of product $1$ and $$4$ per unit of product $2.$

Each plant has the same two production processes, each of

which can be used to produce either of the two products. The pro$-$

duction cost per unit produced of each product is shown below for

each process in each plant.