Question

a farmer has 10 acres to plant in wheat and rye. He has to plant at least 7 acres. However, he has only $1200 to spend and each acre of wheat cost $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye if the profit is $500 per acre of wheat and $300 per acre of ry how many acres how many acres of each should be planted to maximize the profit

Answer 1

4 acres of wheat and 4 acres of rye.

Explanation:

Given: Farmer has only 7 acre, he has plant at least 7 acres.

Farmer has only $1200 to spend.

Each acre of wheat will cost $200 and rye will cost $100.

Planting time is only 12 hours

Wheat planting take 1 hour per hour and rye take 2 hours per acre.

Profit on wheat is $500 per acre and rye $300 per acre.

As to find out maximum profit, we need to plant maximum wheat.

While dividing number of acres of land for wheat and rye for plantation, we need to keep two constraint in the mind; Constraint of cost and time as given.

Lets assume few number considering these constraint to get maximum profit.

First assumption, 5 acres of wheat and 2 acres of rye

Time taken=
`5* 1= 5 h\\2* 2= 2 h`

Total time taken 7 hours

Amount spent=
`5* 200= \$ 1000\\2* 100= \$ 200`

Total cost is $ 1200.

Profit=
`5* 500= \$ 2500\\2* 300= \$ 600`

Maximum profit= $3100.

Second assumption, 4 acres of wheat and 4 acres of rye.

Times taken=
`4* 1= 4 h\\4* 2= 8 h`

Total time taken is 12 hours

Amount spent=
`4* 200= \$ 800\\4* 100= \$ 400`

Total cost is $1200.

Profit=
`4* 500= \$ 2000\\4* 300= \$ 1200`

Maximum profit= $3200.

∴ By using hit and trail method, we can see that we are getting maximum profit when farmer is planting 4 acres of wheat and 4 acres of rye.