The first, type A, costs $267 and you make a $24 profit on each one.
The second, type B, costs $127 and you make a $20 profit on each one.
number of printers = 170
Let x be the number of type A printers
Let y be the number of type B printers
x + y < = 170
you need to make at least $3760 profit on them
profit for type A is 24 and type B is 20
so 24x + 20y >= 3760
Our constraints are
x + y < = 170
24x + 20y >= 3760
x>=0 and y>=0
Cost function is C= 267 x + 127 y
Now we graph all the constraints
Now we take all the end points
corner points are
(90,80), (156.667,0) (170,0)
We plug in each point in our cost function
C= 267 x + 127 y
(90,80) => 267(90) + 127(80) = 34,190
(156.667,0) => 267(156.667) + 127(0) = 41,830
5 (170,0)=> 267(170) + 127(0) = 41,390
Here minimum cost is 34,190 at (90,80)
So we order 90 printers of type A and 80 printers for type B in order to minimize the cost
