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Evgesh-ka [11]
4 years ago
11

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?

Mathematics
2 answers:
Ksju [112]4 years ago
7 0
Let x represent the number of A printers 
<span>Let y represent the number of B printers </span>

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

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

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

<span>The best result is x = 100 and y = 0</span>
qaws [65]4 years ago
4 0

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.

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