need your assistance!

[wmosley2]

Can someone help me with this?




Cost Control...

An appliance repair shop has 5 vacuum cleaners, 12 TV sets, and 18 VCRs to be repaired. The store employs two part-time repairmen. One repairman can repair one vacuum cleaner, three TV sets, and three VCRs in 1 week, while the second repairman can repair one cacuum cleaner, two TV sets and six VCRs in 1 week. The first employee is paid $250 a week and the second employee is paid $220 a week. To minimize the cost, how many weeks should each of the two repairmen be employed?

[alkatran]

Step 1: Change the problem into a formula
Need to repair: (5,12,18)
A -> Number of weeks with repairman one (1,3,3)
B -> Number of weeks with repairman two (1,2,6)

They both have (1,#,#) so we'll eliminate vacuums and say the minimum number of weeks is 5:
A + B >= 5
Also, for TVs and VCRs:
3A + 2B >= 12
3A + 6B >= 18 == A + 2b >= 9

Since we have two equations with 2b, might as well make the first as well:
A + 2B >= 9
2A + 2B >= 5
3A + 2B >= 12
and also:
A >= 0
B >= 0

Now, the easiest way to solve this is: Plot a graph of all these limits and shade the spots that aren't allowed. Then check all the points where limits intersect. One of them will be the best answer.