A maths puzzle is as follows:
Bonger have a printing budget of $119.40. Bonger have 5 children. Each children may do some printing, subject to the printing limit that their father impose, at any day(s) in a period of 365 days.
There is a company who provide printing services, which user buy any of their Printing Card, which is as follows:
Printing Card A: can print max 30 pages for a period of 3 days only for $2
Printing Card B: can print max 200 pages for a period of 3 days only for $4
Printing Card C: can print max 1000 pages for a period of 7 days only for $7
Printing Card D: can print max 2400 pages for a period of 30 days only for $15
Printing Card E: can print max 3600 pages for a period of 30 days only for $20
I try solving the puzzles by finding the total cost for at least 365 days when purchase X amount of same type of Printing Cards, as follows:
Buying 122 Printing Card A - which result in 366 days and max 3,660 pages and cost $244
Buying 122 Printing Card B - which result in 366 days and max 24,400 pages and cost $488
Buying 53 Printing Card C - which result in 371 days and max 53,000 pages and cost $371
Buying 13 Printing Card D - which result in 390 days and max 31,200 pages and cost $195
Buying 13 Printing Card E - which result in 390 days and max 46,800 pages and cost $260
Based on the calculation above, neither one can fit in Bonger budget.
So, I reduce each Printing Card by one, as follows:
Buying 121 Printing Card A - which result in 363 days and max 3,630 pages and cost $242
Buying 121 Printing Card B - which result in 363 days and max 24,200 pages and cost $484
Buying 52 Printing Card C - which result in 364 days and max 52,000 pages and cost $364
Buying 12 Printing Card D - which result in 360 days and max 28,800 pages and cost $180
Buying 12 Printing Card E - which result in 360 days and max 43,200 pages and cost $240
Based on the calculation above, neither one can fit in Bonger budget. Also, there are some days which Bonger children would not be able to do printing.
So, what should Bonger do such that he can have fulfill the following requirements:
Not exceed his budget
Min. days affected, which result in Bonger children would not be able to do printing.