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

You want to

minimize C=86A+130B
subject to
A+B >= 100
45A + 35B >= 3850

Now use your LP tools

Answer 2

To determine the quantity of each type of printer that you should order in order to minimize your cost, we need to set up a mathematical model and then solve it.

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

The cost of each type A printer is $86, so the total cost of x type A printers is 86x.
The cost of each type B printer is $130, so the total cost of y type B printers is 130y.

Therefore, the total cost of all the printers is:
Total Cost = 86x + 130y

To determine the minimum cost, we need to minimize this cost function. However, we also have some constraints.

1. You expect to sell at least 100 laser printers this month, so the total quantity must be greater than or equal to 100:
x + y ≥ 100

2. You need to make at least $3850 profit on the printers:
Profit = 45x + 35y ≥ 3850

Now, we can graph these constraints on a coordinate plane to visualize the feasible region. The feasible region will be the region where both the constraints are satisfied.

Once we have the feasible region, we need to find the corner point(s) (if any) that minimize the cost function. These corner points will give us the quantities of printers that will minimize the cost.

To find the corner point(s), we can use various methods like graphical method, substitution method, or linear programming methods like simplex algorithm or graphical method.

It is recommended to use computer software or spreadsheets to solve such problems, as they can quickly solve optimization problems by inputting the mathematical model and constraints.

By solving this problem mathematically or using optimization software, you will obtain the specific quantities of each type of printer that will minimize your cost in order to meet the profit requirement.