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Alex is a writer who writes poems and short stories. For an upcoming writer's workshop Alex is getting paid to write some new works. He earns $100 for each poem and $250 for each short story he writes for the workshop. Alex figures that each poem will take him 30 hours and each short story will take him 70 hours.  For the workshop Alex wants to have at least 4 poems and 3 short stories to display.  If Alex has 840 hours of work time available, how many poems and short stories should he write to maximize his profit?

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 Jan 13, 2023
 #1
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LCM(30, 70) ==210 hours

 

210 hours / 30 hours ==7 poems - he can write

7  x  $100 ==$700 - he can earn from 7 poems

 

840 hours  -  210 hours ==630 hours left

630 hours /70 hours ==9 short stories he can write.

9  x  $250 ==$2,250 he can earn from 9 short dtores.

 

So then, he should write: 7 poems + 9 short stories ==16

His total earning from the 16 works: $700  +  $2,250 ==$2,950

 Jan 13, 2023

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