Question

Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you mame a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost?

Answer 1

Let x represent the number of A printers 
Let y represent the number of B printers 

Minimize cost = 86x + 130y 
subject to 
Total printers equn: x + y ≥ 100 
Total profit equn: 45x + 35y ≥ 3850 
x ≥ 0, y ≥ 0 
x and y must be whole numbers. 

The vertices of the feasible region are: (0, 100), (100, 0) and (35, 65) 

If x = 35 and y = 65 the cost is 11460 and profit is 3850 
if x = 100 and y = 0 the cost is 8600 and profit is 4500 
If x = 0 and y = 100 the cost is 13000 and profit is 3500 

The best result is x = 100 and y = 0

Answer 2

Answer:

100 printers of Type A

Step-by-step explanation:

Let x be the no. of printers of type A

Let y be the no. of printers of type B

You expect to sell at least 100 laser printers this month

Equation becomes : $x+y\geq100$   ---1

Cost of 1 printer of Type A = $86

Cost of x printer of Type A = $86x

Cost of 1 printer of type B  =$135

Cost of y printer of type B  =$135 y

Minimize cost function: $86x+130y$

Now Profit on 1 Type A printer = $45

Profit on x Type A printer = $45x

Profit on 1 Type B printer = $35

Profit on y Type B printer = $35y

We are given that you need to make at least $3850 profit on them.

So, equation becomes : $45x+35\geq 3850$ ---2

Conditions : $x\geq 0$ ---3 and $y\geq 0$ ---4

Now plotting the lines 1,2,3,4 on the graph

Refer the attached figure

Feasible points are (100,0);(0,100)and(35,65)

Now check which feasible point provides minimum cost.

$86x+130y$

At point (100,0)

$86(100)+130(0)$

$8600$

So, At point (100,0) total cost is $8600.

At point (0,100)

$86(0)+130(100)$

$13000$

So, At point (0,100) total cost is $13000

At point (35,65)

$86(35)+130(65)$

$11460$

So, At point (35,65) total cost is $11460

So, at (100,0) we are getting the minimum cost i.e. $8600.

So, we need to order 100 printers of type A and 0 printers of type B to  minimize the cost.