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?

P= 86x +130y
Constraints: x + y ≥ 100
45x+35y ≥ 3850

Please help me solve this..This is a linear programming problem..

Answer 1

X type A printers.
Y type B printers.

Eq1: x + y => 100.
Eq2: 45x + 35y => 3850.
Multiply Eq1 by -35 and add the Eqs:

-35x - 35y => -3500.
+45x + 35y => +3850.
10x => 350, X => 35 Type A printers.

In Eq1, replace x with 35:
35 + y => 100, Y => 65 Type B printers.