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Help.

NotSoSmart  Oct 12, 2017
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 #1
avatar+79819 
+1

These are always a little difficult, NSS....

Note that we make a $22 profit on the Type A printer and a $19 profit on the Type  B printer

And we can order no more than 120 total in one one month

Let x  be the number of Type A printers and y be the number of Type B printers

 

So.....we have these constraints

 

22x+ 19y ≥  2400  and

x + y  ≤ 120

 

And we wish to minimize the cost function given by

 

237x +  122y

 

Here's a graph of the constraints : https://www.desmos.com/calculator/qz01ip2whh

 

Note that the minimum cost occurs at the corner point corner point (40,80)  

 

And that cost is    237(40) + 122(80)  = $19240

 

So.....we should order 40 Type A printers and 80 Type B printers

 

 

cool cool cool

CPhill  Oct 12, 2017
 #2
avatar+79819 
+1

Here's the second one :

 

"y can exceed x by no more than 200 units"......this is a fancy way of saying that

 

y - x  ≤ 200   

 

and  we know that

 

x + 2y ≤ 1600

 

And we wish to maximize this

 

14x + 22y - 900

 

Here's a graph of the constraints : https://www.desmos.com/calculator/dgtafe0gd7

 

Note that the max profit is found at the corner point (400, 600) ....this will always be true.....the max - or min - will always occur at a corner point....!!!!!!

 

 

cool cool cool 

CPhill  Oct 12, 2017

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