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?

Type A has lower costs, and more profit each. If you sell 100 of them, you make 4500 dollars.

There is no way buying any type B can mimize cost.

Either you copied this problem wrong, or the author was either not thinking, or has no command of the subject of basic calculus.

To solve this problem, we need to determine the number of printers of each type that will minimize the cost while meeting the given profit requirement.

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

The cost of type A printers is $86 each, and the profit per printer is $45. Therefore, the total cost for type A printers is 86x, and the total profit is 45x.
Similarly, the cost of type B printers is $130 each, and the profit per printer is $35. So, the total cost for type B printers is 130y, and the total profit is 35y.

We know that we need to make at least $3850 in total profit, so we can set up the equation:
45x + 35y ≥ 3850

We also know that we need to sell at least 100 printers in total, so we have the constraint:
x + y ≥ 100

To minimize the cost, we need to minimize the total cost, which is:
Total Cost = Cost of type A printers + Cost of type B printers
Total Cost = 86x + 130y

Now, we can solve this linear programming problem using the Simplex method or a graphical method. However, in this case, we can solve it directly by inspection.

Let's consider the constraint x + y ≥ 100. To minimize the cost, we want to use the minimum number of type A printers, as they have a lower cost. To do this, we can set y to its lowest possible value, which is zero. Plugging this into the constraint, we have x + 0 ≥ 100, which gives us x ≥ 100. So, the minimum value of x is 100.

Next, let's consider the constraint 45x + 35y ≥ 3850. Using the values we obtained above, we have 45(100) + 35(0) ≥ 3850, which simplifies to 4500 ≥ 3850. This inequality holds true.

Therefore, by ordering 100 type A printers and 0 type B printers, we can meet the minimum profit requirement and minimize the cost.