For The Mathematically Inclined

A factory that produces tables and chairs is equipped with 10 saws, 6 lathes, and 18 sanding machines. It takes a chair 10 minutes on a saw, 5 minutes on a lathe, and 5 minutes of sanding to be completed. It takes a table 5 minutes on a saw, 5 minutes on a lathe, and 20 minutes of sanding to be completed. A chair sells for $10 and a table sells for $20. How many tables and chairs should the factory produce per hour to yield the highest revenue, and what is that revenue?

PROBLEM #2

You have a 6 foot fence and at 15 foot board. The sun is shining directly overhead. You want to lean your board against the fence so that as large a shadow as possible covers your neighbor's yard. What is the maximum length of the shadow you can form? The ladder must rest against the fence and touch the ground on your side of the fence.

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Problems from 06/06/13

PROBLEM #1
If it takes Bill 20 hours to paint a house and it takes George 30 hours, how long will it take if they work together yet independently?

SOLUTION 1
12 h.

PROBLEM #2
A large tank has a steadily flowing intake and 10 outlet valves, the latter being all of the same size. With 10 outlets open, it takes two and one half hours to empty the tank; with 6 outlets open it takes five and one half hours to empty the tank. After the tank is empty and with all 10 outlets closed, how long will it take to fill the tank?

SOLUTION 2
6.875 h.

Congratulations to Kishore Balsara, Saba Lateef and Suhas Pathak, who were the winners of the last set of puzzles.