For The Mathematically Inclined

PROBLEM #2

What is the y-intercept of the line that is tangent to the curve
y = -2x^3+3x at (1,1) ?

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Problems from 06/20/13

PROBLEM #1
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?

SOLUTION 1
24 chairs and 48 tables - $1,200.

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.

SOLUTION 2
4,636 ft.

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