Optimizing Oz Jeans Manufacturing Costs: Mydney & Selbourne

[Bushy]

Oz Jeans has factories in Mydney and Selbourne. At the Mydney factory, fixed costs
are \$28 000 per month and the cost of producing each pair of jeans is \$30. At the Selbourne
factory, fixed costs are \$35 200 per month and the cost of producing each pair of jeans is $24.
During the next month Oz Jeans must manufacture 6000 pairs of jeans. Calculate the production order
for each factory, if the total manufacturing costs
for each factory are to be the same.

I have made the Costs equations equal to solve for ‘n’amount of jeans to get 1200. I.e 28000+30n = 35200+24n, then substituted these back into the Cost equations for each factory. The Answer says 2400 and 3200 which gives the 6000 in thequestion, but I can’t find how they got it..?

 

[Evgeny.Makarov]

The equation is
\[
28\,000+30x = 35\,200+24(6000-x).
\]
The solution is $x=2800$, so $6000-2800=3200$.

 

[Bushy]

I found it.

a+b=6000
and
30a+28000 = 24y+35200

gives the solution.