13 A school has orders for 200 red 500 black and 100 green c

13. A school has orders for 200 red, 500 black, and 100 green color marking pens. Marking pens come in two different combinations of color. Box A contains 10 red and 2 green pens and costs $10 per box, Box B contains 20 black and 1 green pens and costs $15 per box. How many boxes of each should be bought in order to minimize the cost?

Solution

a school orders for 200 red ,500 black, and 100 green pens

here box A contains

10 red and 2 green pens and costs $10 per box                                      (1)

and box B contains

20 black and 1 green pens and costs $15 box                                              (2)

school requires  200 red ,500 black, and 100 green pens

multiply 1 by 20 we get

200red+40 green=10*10                                             (3)

multiply (2) by 25 we get

500black+25 green=15*25                                       (4)

adding 3 and 4 we get

200red+500black+65 green =100+375=475

for A requires 10 such boxes

and box B requires 25 boxes

tota bpxes brought is l 10+25<=35