#1**+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

CPhill
Oct 12, 2017

#2**+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....!!!!!!

CPhill
Oct 12, 2017