Jahee manages two departments at a printer plant: one department assembles the printers and one packages them for shipment. Jahee knows that it take 0.25hrs to assemble each inkjet printer and 2 hrs to assemble each laser printer. She has allotted no more than 120 hours for assembly. She also knows that it takes 1.25 hrs to pack each inkjet printer and 0.5 hrs to pack each laser printer. She has allotted no more than 40 hours for packing. Write and graph a system of inequalities to represent the possible combinations of printers the plant can produce.

Question

anonymous · Answer

x = # inkjets 
y = # lasers 

Assembly time for inkjets = 0.25x 
Assembly time for lasers = 2y 
Max assembly time = 120
$$0.25x+2y≤120$$
packing time for inkjets = 1.25x
packing time for lasers = 0.5y
max packing time = 40
$$1.25x+0.5y≤40$$
both amounts have to be positive, so
$x≥0$ and $y≥0$