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The 90 turkeys (Posted on 2008-11-27) Difficulty: 2 of 5
Last December, at Christmas Eve, Nagib called his three sons, Abdon, Fairuz and Samara, and gave them 90 turkeys to be sold at the fair.

- "Abdon, you will carry 10 turkeys. You, Fairuz, will carry 30 turkeys, and Samara the remaining 50 turkeys, and each one of you has to bring me $1,500 after selling all the turkeys.

Abdon is free to devise the strategy you all will use, that is, the price of one turkey established by Abdon for a group of turkeys must be exactly the same that you two have to follow.

Explaining better a two-step strategy: if Abdon decides to sell 4 of them by $1200 ($300 each), you two must sell any quantity you want, but by the same unit price ($300 each turkey). Then, if Abdon decides to sell the remaining 6 turkeys he has by $300 ($50 each), you two must sell your remaining turkeys by this same unit price ($50 each turkey).

But, I am not forcing that the strategy devised by Abdon must consist of only two steps. I gave you just an example which, by the way, doesnīt work for what I want. Moreover, in the strategy devised, in each step all three must sell at least one turkey, by an unitary price greater than zero."

What is the strategy devised by Abdon to insure that each one gathers exactly $1,500 for the turkeys they carried to the fair?

  Submitted by pcbouhid    
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Solution: (Hide)
Though Charles and rod exausted the solutions, I still donīt see how to solve this analytically, because we donīt know for sure how many steps are needed.

Anyway, the solution I have (one of the submitted) is:

1) First step: 7 turkeys at $150.

(A) sells 7 turkeys by $150.
(F) sells 28 turkeys by 28/7 * 150 = $600
(S) sells 49 turkeys by 49/7 * 150 = $1,050.

2) Second step: each remaining turkey at $450.

(A) sells 3 turkeys by 3*$450 = $1, = $150 + $1,350 = $1,500.
(F) sells 2 turkeys by 2*$450 = $ = $600 + $900 = $1,500.
(S) sells 1 turkey by $ = $1,050 + $450 = $1,500.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: An observation!pcbouhid2008-12-04 08:00:46
An observation!rod hines2008-12-03 17:29:11
re(3): additional solution for non-whole dollar prices - missing somethingpcbouhid2008-12-03 14:57:53
Solutionre(2): additional solution for non-whole dollar prices - missing somethingCharlie2008-12-03 13:32:19
re: additional solution for non-whole dollar prices - missing somethingpcbouhid2008-12-03 12:46:31
Solutionadditional solution for non-whole dollar pricesCharlie2008-12-02 18:49:12
Solutionall 2-step solutions with integral dollar pricesCharlie2008-12-02 18:44:04
re(4): two-stepspcbouhid2008-12-02 17:39:33
re(3): two-stepsrod hines2008-12-02 14:23:05
re(2): two-stepspcbouhid2008-12-02 13:43:07
re: two-stepsrod hines2008-12-02 13:01:02
two-stepspcbouhid2008-12-02 11:24:46
Possible Solutionrod hines2008-11-27 18:49:40
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