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, doesn´t 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?

(In reply to re: additional solution for non-whole dollar prices - missing something by pcbouhid)

ok:

First row in each case shows A's first and second revenues, and then the common first and second unit prices. Next 3 rows show respectively, A's, F's and S's quantities sold.

 15            1485          15            165
 1             9
 23            7
 45            5

 30            1470          10            210
 3             7
 24            6
 45            5

 56.25         1443.75       18.75         206.25
 3             7
 25            5
 47            3

 1350          150           450           21.42857142857143
 3             7
 2             28
 1             49

 1400          100           350           16.66666666666667
 4             6
 3             27
 2             48

 125           1375          25            275
 5             5
 27            3
 49            1

But if each turkey is sold to a different customer, the unit prices that have fractional pennies would not be possible.

DEFDBL A-Z
CLS
FOR an1 = 1 TO 5
 an2 = 10 - an1
 ap1 = 1
 DO
   ap2 = (150000 - ap1)
   IF ap2 < 1 THEN EXIT DO
     FOR bn1 = 1 TO 29
       bn2 = 30 - bn1
       IF bn1 * ap1 * an2 + bn2 * ap2 * an1 = 150000 * an1 * an2 THEN
          FOR cn1 = 1 TO 49
            cn2 = 50 - cn1
            IF cn1 * ap1 * an2 + cn2 * ap2 * an1 = 150000 * an1 * an2 THEN
               PRINT ap1 / 100, ap2 / 100, ap1 / (100 * an1), ap2 / (100 * an2)
               PRINT an1, an2
               PRINT bn1, bn2
               PRINT cn1, cn2
               PRINT
            END IF
          NEXT
       END IF
     NEXT
   ap1 = ap1 + 1
 LOOP
NEXT an1

 

Posted by Charlie on 2008-12-03 13:32:19