Answer:
45 inkjet printers and 25 laser printers should be made to give maximum profit.
The maximum profit is $3750
Step-by-step explanation:
Let x be the no. of inkjet printers
Let y be the no. of laser printers
The company has the capacity to make 70 printers per day
So,[tex]x+y\leq 70[/tex]---1
Time taken to make 1 inkjet printer = 1 hour
So, Time taken to make x inkjet printer = x hour
Time taken to make 1 laser printer = 3 hours
So, time taken to make y laser printers = 3y hours
It has 120 hours of labor per day available
So, [tex]x+3y\leq 120[/tex] ---2
The profits are $50 per inkjet printer and $60 per laser printer.
So, P=50x+60y
Where P is the profit function
Plot the lines 1 and 2 on the graph
[tex]x+y\leq 70[/tex]
[tex]x+3y\leq 120[/tex]
Such that the [tex]x\geq 0 , y\geq 0[/tex]
Now the boundary points of feasible region are (0,40),(45,25) and (70,0)
Substitute the points in the profit function
At (0,40)
P=50x+60y
P=50(0)+60(40)
P=2400
At (45,25)
P=50x+60y
P=50(45)+60(25)
P=3750
At (70,0)
P=50x+60y
P=50(70)+60(0)
P=3500
So, we got the maximum profit at (45,25)
So, 45 inkjet printers and 25 laser printers should be made to give maximum profit.
The maximum profit is $3750
