Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make 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?

Question

Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make 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?

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Answer 1

Does anyone know how to solve this?

Answer 2

if you didn`t feed it so often (BE)

Answer 3

To minimize the cost, we need to consider the profit from each type of printer and find the combination that meets the required profit while minimizing the cost.

Let's assume you order x type A printers and y type B printers.

For type A printers:
Profit per printer = $45
Number of Type A printers = x
Cost per Type A printer = $86
Total profit from Type A printers = Profit per printer * Number of Type A printers = 45 * x
Total cost of Type A printers = Cost per Type A printer * Number of Type A printers = 86 * x

For type B printers:
Profit per printer = $35
Number of Type B printers = y
Cost per Type B printer = $130
Total profit from Type B printers = Profit per printer * Number of Type B printers = 35 * y
Total cost of Type B printers = Cost per Type B printer * Number of Type B printers = 130 * y

According to the given conditions:
Total profit from all printers = Total profit from Type A printers + Total profit from Type B printers
Total profit from all printers = $3850

Therefore, we have the equation:
45x + 35y = 3850 ..........(1)

Now, let's consider the constraint that you need to sell at least 100 printers in total:
Number of Type A printers + Number of Type B printers ≥ 100
x + y ≥ 100 ..........(2)

To minimize the cost, we can use a linear programming technique called the simplex method or a graphical method.

However, it is also possible to solve this problem using substitution or elimination method. Let's choose the substitution method:

From equation (2), we have:
y ≥ -x + 100

Substituting this inequality into equation (1):
45x + 35(-x + 100) = 3850
45x - 35x + 3500 = 3850
10x = 350
x = 35

Substituting the value of x back into equation (2):
35 + y ≥ 100
y ≥ 100 - 35
y ≥ 65

Therefore, the minimum cost combination of printers that meets the profit requirement is to order 35 type A printers and at least 65 type B printers.