A farmer is deciding how much corn, soybeans, and wheat to plant in the

coming growing season. The following table shows expected crop yields and

expected contributions towards fixed costs per bushel for each crop:

$(10$pt$)$ RainALot Irrigation, Inc., would like to determine capacity requirements

for the next four years. Currently two production lines are in place for making

bronze and plastic sprinklers. Three types of sprinklers are available in both

bronze and plastic: $90-$degree nozzle sprinklers, $180-$degree nozzle sprinklers,

$360-$degree nozzle sprinklers. Management has forecast demand for the next four

years as follows:

YEARLY DEMAND

$1($IN

$000$s$)$

$2($IN

$000$s$)$

$3($IN

$000$s$)$

$4($IN

$000$s$)$

Plastic $9032445556$

Plastic $18015161718$

Plastic $36050556467$

Bronze $9078910$

Bronze $1803456$

Bronze $36011121518$

Both production lines can produce all the different types of nozzles. Each bronze

machine needed for the bronze sprinklers require two operators and can produce up

to $12,000$ sprinklers. Each plastic injection molding machine needed for the plastic

sprinklers require four operators and can produce up to $180,000$ sprinklers. Three

bronze machines and only one injection molding machine are available. What are

the capacity requirements for the next four years?