Optimization Problem

ffuh205

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Mar 17, 2010
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A farmer wants to hire workers to pick 900 bushels of beans. Each worker can pick 5 bushels per hour and is paid $2 per bushel. The farmer must also hire a supervisor at $10 per hour while the picking is in progress, and has additional costs of $8 for each worker hired. How many workers should he hire in order to minimize the total cost? What will be his total costs? Draw a graph of the cost function.



Not sure how to procede on this one. There seems to be some variables missing like, how long does he have to pick the beans (is it per day?). Based on the assumption, there only needs to be one but has to be at least one supervisor. So that ($10 + $8x)t for the cost of the workers and ($2*5x)t profit. Not sure where to go from here.
 
ffuh205 said:
A farmer wants to hire workers to pick 900 bushels of beans. Each worker can pick 5 bushels per hour and is paid $2 per bushel. The farmer must also hire a supervisor at $10 per hour while the picking is in progress, and has additional costs of $8 for each worker hired. How many workers should he hire in order to minimize the total cost? What will be his total costs? Draw a graph of the cost function.



Not sure how to procede on this one. There seems to be some variables missing like, how long does he have to pick the beans (is it per day?). Based on the assumption, there only needs to be one but has to be at least one supervisor. So that ($10 + $8x)t for the cost of the workers and ($2*5x)t profit. Not sure where to go from here.

You cannot calculate profit - we have no information about revenue. We can only deal with cost part.

No. of workers hired = x

No. of hours worked by each worker = W

W * x * 5 = 900 ? W = 180/x ? There is your no. of hours worked.

No. Bushels each worker will pick = B = 900/x

Can you develop your cost function now?
 
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