Question

Your computer supply store sells two types of inkjet printers. The first, type A, costs $269 and you make a $24 profit on each one. The second, type B, costs $173 and you make a $18 profit on each one. You can order no more than 120 printers this month, and you need to make at least $2340 profit on them. If you must order at least one of each type of printer, how many of each type of printer should you order if you want to minimize your cost?

Answer 1

This is the concept of applications of linear equations; suppose you need x number of type A and y number of type be to make the profits required;
Total number of printers will be:
x+y=120....i
Total amount made will be:
24x+18y=2340....ii
thus solving equations i and ii by substitution we shall have:
x+y=120
x=120-y
thus substituting the above in equation ii we get:
24(120-y)+18y=2340
2880-24y+18y=2340
putting like terms together we get
-24y+18y=2340-2880
540=6y
thus
y=540/2
y=90
hence;
x=120-90=30
Therefore to make the profit of $2340 you must sale 90 type A printers and 30 type B printers