Question

Newjet, Inc. manufactures inkjet printers and laser printers. The company has the capacity to make 70 printers per day, and it has 120 hours of labor per day available. It takes 1 hour to make an inkjet printer and 3 hours to make a laser printer. The profits are $50 per inkjet printer and $60 per laser printer. Find the number of each type of printer that should be made to give maximum profit, and find the maximum profit.

Answer 1

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,$x+y\leq 70$---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, $x+3y\leq 120$  ---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

$x+y\leq 70$

$x+3y\leq 120$

Such that the $x\geq 0 , y\geq 0$

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