A town has a merchant, a baker, and a farmer. To produce $1 worth of output, the merchant requires $0.15 worth of baked goods and $0.35 worth of the farmer's products. To produce $1 worth of output, the baker requires $0.45 worth of the merchant's goods, $0.20 worth of his own goods, and $0.35 worth of the farmer's goods. To produce $1 worth of output, the farmer requires $0.25 worth of the merchant's goods, $0.25 worth of baked goods, and $0.30 worth of his own products. How much should the merchant, baker, and farmer produce to meet a demand for $18 comma 000 worth of output from the merchant, $11 comma 000 worth of output from the baker, and $12 comma 000 worth of output from the farmer?

Merchant: $7950

Baker: $7900

Farmer: $13750

Step-by-step explanation:

To produce $18000 worth of output from merchant we would need

- $18000*0.15 = $2700 worth of product from the baker

- $18000*0.35 = $6300 worth of product form the farmer

To produce $11000 worth of output from the baker we would need

- $11000*0.45 = $4950 worth of product from the merchant

- $11000*0.2 = $2200 worth of product from himself

- $11000*0.35 = $3850 worth of product form the farmer

To produce $12000 worth of output from the farmer we would need

- $12000*0.25 = $3000 worth of product from the merchant

- $12000*0.25 = $3000 worth of product from the baker

- $12000*0.3 = $3600 worth of product form the himself

In total:

The merchant would need to produce: $4950 + $3000 = $7950

The baker would need to produce: $2700 + $2200 + $3000 = $7900

The farmer would need to produce: $6300 + $3850 + $3600 = $13750