MHB Optimizing Oz Jeans Manufacturing Costs: Mydney & Selbourne

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Oz Jeans operates factories in Mydney and Selbourne, with fixed costs of $28,000 and $35,200 respectively, and variable production costs of $30 and $24 per pair of jeans. To achieve equal total manufacturing costs while producing 6,000 pairs, the production order must be calculated. The equations set for cost equality lead to the solution of producing 2,800 pairs in Mydney and 3,200 pairs in Selbourne. This distribution maintains the total production requirement while balancing costs. The calculations confirm the production order for each factory.
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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..?

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

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

gives the solution.
 
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