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your computer supply store sells two types of laser printers. the first type, a, costs $137 and you make a $50 profit on each one. the second type, b, costs $110 and you make a $40 profit on each one. you expect to sell at least 100 laser printers this month and you need you make at least $4400 profit on them. if you must order at least one of each type if printer, how many of each type of printer should you order if you want to minimize your cost?

Respuesta :

Louli
Let the number of units of the first type be x and the number of units of the second type be y.

A. You expect to sell at least 100 printers this month. This means that:
A + B >= 100 
For simplicity, we will work on the equal sign (A + B = 100) which is the minimum number of units to be sold.
This can be rewritten as: A = 100 - B .................> equation I

B. You expect to make a minimum profit of 4400. This means that:
50A + 40B >= 4400
Again for simplicity, we will work on the equal sign (50A + 40B = 4400) which is the minimum profit to be made
50A + 40B = 4400 ..................> equation II

Substitute with equation I in II:
50 (100-B) + 40B = 4400
5000 - 50B + 40B = 4400
5000 - 4400 = 50B - 40B
600 = 10B
B = 60
Substitute in equation I:
A = 100 - B = 100-60 = 40

Therefore, to minimize your cost and achieve your goals in number of selling units and profits:
you should buy at least 40 units from the first type and 60 units from the second type

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