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stiv31 [10]
3 years ago
10

Newjet, Inc. manufactures inkjet printers and laser printers. The company has the capacity to make 70 printers per day, and it h

as 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.

Mathematics
1 answer:
Nuetrik [128]3 years ago
6 0

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

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